I started testing this game in june. My first impress was 'WOW. It's amazing!' and then I imagined that why don't I do a speedrun?
So I was trying, playing looking for glitches day by day. The game itself is not hard. You don't need to watch your health bar or your ammo if you play on easy.
You cannot go fast. Nothing boost you just monsters. You are not able to jump over things to reach the map changer trigger as fast as you can.
The game has weird scripting and things aren't working as you remember from your last try.
I would be glad to render thanks but... nobody helps me. There are only two person but at two point of the map that means every glitch, trick that is well known from now was my idea.
The following segments are named by savegame names.

l00_intro:
Firstly, I run through Miller and quickly open the gate. You need to pick up three ammo and a medkit.
I was quick therefore Miller is teleported to the next event. I go up and kill the mutant. After that I have to be very quick.
I kill the first mutant and then I riddle the next two with bullets because if I am not enough fast, another mutant appears. (I'm not sure)
Then I run toward the tower to get the cutscene. (thanks to ZhouTai)
Finally I must wait. There is no chance to finish it faster.

l01_hunter:
I go up to the hall and kill the mutants. The first group goes front the ceiling, the next one is from the left air-duct and the last scripted mutant goes from the right.
After that they come from random places but if you are lucky, there won't be so many. I think it doesn't depend on how many mutants you kill.

l02_exhibition:
I just have to be quick to avoid sharp edges. You can go through the first man if you choose a good angle but the second man block you whatever you do. At the gunstore, I am stucked for half a second but the shopman starts speaking that means everything goes right.

l03_chase:
There is no place for improvement. The only thing that can happen is a zoom effect (after you come out the cover) that moves you 2-3 meters toward.

l04_riga:
I pick up the money, run to Bourbon and after discussing I go next to the toilets because Bourbon would stop if you were not there.
Then I buy 3 grenades. I try the red ammunition box but there was no ammo in my video. But there are rarely existing.
The level ends when Bourbon goes through the door so I didn't have time loss.

l05_lost_tunnel:
I had four grenades. It is enough for bandits. I go through the tunnel and wait for Bourbon. I missed the wire so I had to redo it but I didn't miss any seconds.
One grenade for the camp, one for the guard and the last two or three are easy to kill. I lost a second because the last door opens automatically and I didn't recognise that.

l06_bridge:
This is the only place where I had bug. My gun stayed on the screen and the other one also appeared but It didn't make the run longer so... I kill every mutant and bypass the train for... fun. After that We know We cannot jump to the door. I presented It in the Metro 2033 thread.

l07_catacombes:
I collect all the ammunition. After the dreamy scenes, I reach the big door. Bourbon arrive and We start shooting the mutants.
I don't know how is it timed but I have no idea to shave off time. You have to be with him but shooting skill doesn't help.
There you have to crouch and go through the big door but this information is come up after I uploaded the video. (thanks to kekskiller)

l08_market:
I run to the shop and imitate that I buy something. It moves Bourbon to the next event. After that I go to the gate and wait for Bourbon.

l09_dead_city_1:
I don't waste my time jumping on the car so I go to the end. This is a big place but I cannot find any improvements.

l10_dead_city_2:
The screen is black but I memorized the way to get outside. (skillful trick uh..?) I walk to the truck and wait for the demon.
I throw a grenade and hopefully It kills it. This trick skip a little section of the following events.
After that I kill some mutants and climb up to the fence. You can see I do this because I can reach the well quicker.

l11_dry:
Easiest segment. I just found the best way to get out of there. I don't need to kill anyone or avoid shots.

l12_ghosts:
The first two ghosts can be avoided but the guard cannot. Wait for them to move to the sides. After that I just run.

l13_anomaly:
At the end, the anomaly hit the door and I run to the railcar. It force khan to jump to the next event.

l14_cursed:
This is a very ugly part of the run. I did everything correctly but It seems there is another improvement but I didn't know anything about it.(Kekskiller -10sec)

l15_armory:
Nothing special but I bought new kevlar clothes for the next level.

l16_frontline:
Very primitive way to run through the map but I cannot find any quicker way.

l17_trolley_combat:
I cannot bypass Pavel so I missed 1-2 seconds.

l18_depot:
I must kill the Nazi to go through the station silently.

l19_defence:
Very annoying part. I tried everything but the only place where You can clim up is the top of the iron box where the boss stays. So I must fight.

l20_child:
It's hard to move the mouse but there was no problem.

l21_nazi_outpost:
I choose the quickest route and It works well. Tip: Going out the map is longer with 10 seconds

l22_black:
'Sneaking through the shadow...' Quickest route, no problems.

l23_polis:
I have to stay to Miller because It starts the next event.

l24_alley:
Nothing special.

l25_library:
When I am in, I have to run to the door but there is a Librarian, and It block your way. You cannot cut the route.
After that I shoot the luster to skip the demon cutscene.

l26_archives:
Nothing special.

l28_depository:
First and last ladder jump works well. Then I go through the map as fast as I can.

l27_driving:
Nothing special.

l30_darkstar:
Nothing special.

l31_catacombes:
Nothing special.

l32_cave:
Nothing special.

l33_d6:
Most boring and longest part of the game. You cannot run down to the lower floors. The generators broke down randomly.
Your mate stucks everywhere at the lowest floor. So I mustn't kill the mothers of the giant ameoba because He would be just standing.

l34_biomass:
The floor is covered with annoying oranges and It is the true chaos.
After that I use the crane and it looks bad but I lost just one or two seconds. And I was hesitating after It, but I was just careful.
You can quickly fall down and die.

l35_division: Nothing special.

l36_ostankino: Nothing special. The same as the first segment but then You have to wait for Miller sometimes.

l38_tower: Hardest part of the game. You can stuck in everything and It's hard to navigate your mouse.

l39_ethereal: Nothing special. Happy End.

First off, I learned almost everything about running this game from Bebe's WR on Easy difficulty. Without his groundwork, there is no way I could have done this run. He found some things in this game that I never would have found--the invisible wall jump in the 'Archives' segment, for example. (HOW DID HE FIND THAT!?)

Also, shout-out to Sandstormify for finding skips on Bridge and Dead City 1. Those two skips are such a huge time saver. If he hadn't found those, I don't think I would have bothered doing this run.

Oh, and a big thank you to Pabst Blue Ribbon. Without the help trusty help of PBR, I can't imagine how many nights I would've kept attempting to record new segments while being too tired to actually pull them off. With the a can of Pabst by me at all times, I didn't get to be part of the decision of whether I kept playing or not―I just passed out. : D

My run is played on the game's hardest difficulty, Ranger Hardcore. Here's some key points about this difficulty:

*Damage taken is increased tremendously (Artyom will often die instantly)

*Damage done to enemies is also increased, (not tremendously)

*No Cross-hair (unless the weapon has a laser sight)

*No static heads-up display

*Health regeneration takes much longer

*Ammunition is far more scarce. There are the same amount of ammo pick-ups, but the bullets received by the player decrease in amount. On easy and normal, the player picks up ammo in 10s, 15s, etc. On ranger-hardcore, most ammo pickups are 1 to 3 bullets.

The game is full of NPC dialogue scenes, invisible walls and timed/triggered level progression. Where some would see this as an impediment to speed running, I find/found it more enjoyable. When a new skip, glitch, trick, etc is found, it's just that much more rewarding.

A quick note about the spoken languages--The spoken language in the game does in fact affect how fast the levels can be completed. On some segments, the difference between languages was negligible. On other segments, changing the language from English to French, or Russian to English saved fifteen or more seconds.

Segment 1: Prologue

*Snagging at least three ammo pick ups and being ahead of Miller before he reaches the hole in the floor will skip a few lines of his dialogue.

*Kill everything as fast as humanly possible to get to the end of the level.

Segment 2: Hunter

The mutants in the vents spawn in the same order, so there was no real problem there. The second round of mutants that drop from the ceiling were tricky. Sometimes Hunter and the other guy were crack shots and helped pick up the slack, other times they would just kinda...stand there and not shoot. Just took about...you know...40 attempts for the two of them to get their act together and help me out.

Segment 3: Exhibition

Exhibition is a straightforward segment; Run to the armory, get yourself some goodies and then run to the railcar. As fast as possible, of course.

Segment 4: Chase

This was the first level that I (with the help of Sandstormify) found that the audio language directly affected how fast you could get through a level. I had been playing the entire game on Italian (I don't speak Italian, I just like how it sounds) and was consistently getting times that were fifteen (or more) seconds slower than my fellow runner's average times on the level. After some detailed looks at several video clips, I switched the language to English for this segment and BAM! 

Aside from that, it's a very simple level. Shoot the monsters as fast as possible, get to the end of the level...

Segment 5: Riga

I wait for the cut-scene to end...run as fast as possible to Bourbon and trigger him to walk to the end of the level. While he's walking I buy a grenade for future use. Nothing fancy to see here.

Segment 6: Lost Tunnel

The fight with the bandits at the end of this level was arguably one of the hardest parts of this run. The fight can be "activated" sooner than I did in the video by triggering the booby trap in the room connecting the tunnel to the bandit's hideout. If I was playing the game on Easy, I totally would have. On Ranger-Hardcore though...it turned out to be a terrible idea. Fighting the bandits on easy is a walk in the park, damage-wise. For my run though, a few stray bullets (sometimes just one) cause instant death.

So...I came up with a way to take out the majority of the bandits out as quickly and quietly as possible. All but the last two bandits in the main room go down basically right away, and then it's just a matter of gunning down those last two.

The final room of the level, with three bandits, was just as difficult. I ended up just getting really really really lucky. Normally, there is a bandit hiding behind the sandbags at the end of the room. He was such a pain to dispatch quickly while minimizing damage. For some reason, he wasn't hiding there. So...I was able to just run through the room and take the three of them out no problem. (and lucky me, with those three bandits dead, I can open the door to exit the level!)

Segment 7: Bridge

This level was the first big stumbling block I encountered while doing this run.

Sandstormify's discovered that rather than wait like a putz at the end of the level for Bourbon to show up and lower a staircase, one can magically run up the handrail of the raised staircase, jump over it, land on some invisible stuff, and safely make it into the doorway that eventually brings you to the end of the level. This alone saves TONS of time on the level.

I tried to take it a step further with some fancy-schmancy jumps.

I finally succeeded. It only took about two weeks of falling to my death and getting stuck on random scenery (thank you very much object collision). Oh, and if I was able to make it to the new skip without either of those two things happening, my next favorite thing to do was run straight into the staircase (rather than up it) or die from falling damage when trying to make it into that little doorway.

Segment 8: Lost Catacombs

Five minutes of mostly boredom. Please, someone find a way to skip more of these cut-scenes.

After all the cut-scene joy (how 'bout that Great Door? Pretty spooky...) it's all about killing all the mutants as fast as possible to trigger the door opening. Bourbon does some good work here, but if you rely on him too much you lose time.

Segment 9: Market

Nothing special here. Run to merchant, spin around, run back to Bourbon, and then wait to end the level.

Segment 10: Dead City 1

Here's the second skip Sandstormify found. After I saw it, I was like "Man, that was...like hiding something in plain view. It's just right there."

So...Bourbon talks a bunch to a dead body, then he kicks open the door for you. Next we make the jumps to complete the new skip. Then we run to the end of the level.

Managing sprint stamina comes up a few times in the level...as you can only run for so long, dontcha know.

Segment 11: Dead City 2

Throwing a grenade to kill the demon as it lands saves a few seconds here. Timing when to throw the grenade took me a bit longer than I anticipated. It still came out kinda sloppy.

I jump up into the trees and across to the fence a little sooner than Bebe does in the Easy difficulty run. This skips some enemy spawns. There, on top of the fence, we wait for a demon to spawn, crash through the fence, and lead us to the end of the level.

Segment 12: Dry

Nothing fancy here, just running to the end of the level as fast as possible. (There seems to be a reoccurring theme here.)

Try as I might, I couldn't get this segment done any faster than the easy difficulty run. Oh well. Maybe someday.

Segment 13: Ghosts

This level should be called "Waiting for Khan."  With no skips to be found, you just gotta do the old school strat--run from the beginning to end. But we gotta wait for the NPC--you know, that guy who throttles our progress through the level.

Segment 14: Anomaly

Again, nothing fancy here. Just NPC controlled progression. This level has little shooting though, so that's nice.

Segment 15: Cursed

I feel like using grenades here helps thin out the pack of mutants that chases you around.

Just like in the last few levels, this one's just a matter of running to the end, the old fashioned way.

Segment 16: Armory

I pickup the volt-driver laying on the bed after Andrew the Blacksmith saves me from certain capture.

I sell it later, to get money for the stealth suit I need to complete the next level. And I pick up one throwing knife from a merchant as well.

Both the stealth suit and the throwing knife are integral to the upcoming levels.

Segment 17: Frontline

When I was planning out this run, I knew this would be the hardest segment to transition from Easy difficulty to Ranger-Hardcore. It turns out I was right.

After watching how Bebe did the level, it was very clear that I would need to find a new route. (If you don't know what I'm talking about, that means you haven't watched Bebe's run on Easy difficulty. Which means you probably should.)

I spent something like eight days finding a new route through this level. And another four or five days optimizing that route. It took a lot of work and I think it turned out pretty nice.

Lots of jumping around. Sneaking past the Nazis below the train tracks requires a super sensitive touch, good reflexes, and an epic knowledge of how the guard AI works and how they react.

Segment 18: Trolley Combat

The secret strategy for this level? Shoot the enemies before they kill you. That's about all the faster I could make it.

Segment 19: Depot

First, it's super important to shoot the lone guard on the tracks. Your railcar moves through the enemy-occupied areas much faster if he's killed before he can alert the rest of his squad.

Other than that, it's just the standard "shoot all the monsters as fast as possible."  This is one of the levels/segments that I just couldn't seem to find a way to do faster then than Bebe's Easy run.

Segment 20: Defense

Killing as many mutants as fast as possible is the key to this level (as it is to many others.)  The NPC soldiers in the room will do some work, but I don't think the mutants that they kill actually "count" towards progressing the level towards its end.

Segment 21: Child

In this segment, I jump around as much as possible. You cannot sprint during this segment and jumping, especially off of objects makes you travel just a bit faster (I'm pretty sure.)  The jumping, plus the little shortcuts at 0:30 and 0:57 saved me several seconds off the previous time for this segment.

Segment 22: Outpost

This segment was up there with 'Frontline' and 'Lost Tunnels' when it came to being significantly more difficult on Ranger Hardcore than on Easy. Originally, I thought that I was going to have to take a much different approach , since I would have to make it through the bulk of the level undetected by the Nazis in order to survive. Literally. Like, to avoid getting one-shot by the guards. They hurt.

The strategy I found actually required me to go all the way back to the 'Armory' level and replay the game up to there. I just needed a single extra throwing knife to silently take out the Nazi at the top of the staircase at the beginning of the level. With him on ice (Get it? Because it's snowing?), the level is still quite tense. The stealth suit I picked up, also back in the 'Armory,' helps out quite a lot, but running past those guards without getting killed took more attempts and finesse than I ever thought it would.

Segment 23: Black Station

There was no way I was going to make it through this segment undetected by enemies and still beat or tie the record time on the Easy run. I was able to just run and gun my way through with the help of some military grade ammo to quickly dispatch the first few guards in my way. Managing the (invisible) sprint meter was also important, as it carried over from the previous segment, Outpost, where I had almost entirely spent all of Artyom's stamina.

Segment 24: Polis

 There is almost zero player interaction in this level. I was able to shave about ten seconds off the Easy difficulty time for this segment, but I attribute that entirely to using English as the spoken language rather than Russian. I don't feel good about, don't worry.

In all this downtime, I use my military grade rounds to stock up on shotgun shells and tons of dirty ammo for my rifle weapons. A fairly large amount of ammo is needed to deal with the hordes of mutants and other monsters that are encountered in the upcoming levels. Even though the military grade ammunition does more damage, simply having tons of dirty ammo ends up being more efficient when dealing with the large amount of mutants and other monsters that are coming up in the next few segments.

Segment 25: Alley

Nothing of particular note here. Just one of those levels where the player needs to run as fast as possible towards the end of the level.

Segment 26: Library

There's a new time saver here, jumping over the main staircase at 0:40. Other than that, the only real 'tech' in the level is advancing the NPCs as fast as possible by shooting a board blocking a door and shooting down the chandelier.

Segment 27: Depository

Not much to talk about in this segment. Run fast, dodge the Librarians, etc.

Segment 28: Archives

My ladder jump at 0:08 was kinda sloppy, but didn't lose me any real time with a few little microscopic time savers across the level. The invisible wall jump at 0:29 went almost perfectly and a tiny new time saver at 0:44 got me through the level in record time. One minute of speedrunning and one and a half minutes of cutscene―Welcome to Metro 2033.

Segment 29: Driving to Sparta

This level is just a long cutscene, then a few seconds of running...and then more pre-scripted dialogue to end the level. Absolutely nothing of note here.

Segment 30: Darkstar

This segment harkens the arrival of the longest segments of the game;  full of dialogue, pre-scripted NPC-environment interaction, triggered events, etc. I call out to anyone that plays this game―Please help us find new skips!

Like most of the "arenas" in the game―Defense, Dead City 2, Lost Catacombs, and the upcoming segments Dungeon and Cave―Killing enemies as fast as possible is key to advancing the level. Enemies killed by the NPCs don't seem to count towards this goal, but I could be wrong.

I opted to switch back-and-forth from the mounted flame thrower in order to keep dealing as much damage to the mutants as possible while the flamethrower was overheated. I purposely overheat the weapon when I first use it in order to illuminate the tunnel.

Segment 31: Dungeon

This segment is fairly slow and simple. The basic strat for dealing with the game's "arenas" is maintained here. Kill as many enemies as fast as possible, without relying on your NPC comrades.

Segment 32: Cave

More arenas to deal with. This time, it's more difficult, as the number of mutants is the player has to deal with at one time is larger than at any other time during the game.

Segment 33: D6

The best way to describe this segment is with a list:

(I've spent countless hours on this level looking for some way to skip any amount of NPC dialogue/triggers/etc but to no avail. Some sort of skip here could save the run an immense amount of time.)

*Nothing can happen to move the level forward until Miller opens the door to the upper level at 4:00. Until he opens that door there are invisible walls preventing the player from accessing the upper levels.

*The generators break down at random.

*Once the power has been restored and you move deeper into D6, it's possible to shoot several Amoeba pores, thus reducing the amounts of Amoebas that spawn later in the level (and possibly during the Biomass segment.)

*The best/fastest way to kill an Amoeba is with a single shot to its center mass.

*This level is very long, and I wish I could accurately describe the frustration I felt when I would fall to my death while jumping for fun while waiting for the NPCs.

Segment 34: Biomass

This level, by far, was the most difficult (as far as combat goes) in the game. The fight with the bandits in 'Lost Tunnels' was more difficult to pull off, but fighting off the endlessly spawning Amoebas throughout the first portion of this level while also making sure that Miller is constantly and consistently moving forward was absolutely tormenting.

Managing the crane later in the level was clunky and frustrating, especially so since getting to that portion of the level required a well-executed run through all the Amoebas (Damn you Metro 2033 and your lack of quick-saves ruining my ability to grind out difficult parts within single level segments!)

Lowering the crane arm while moving saves some time, but if you lower it too far―or mess with it too much―it becomes sluggish to respond when you need to lower it to remove the rods.

I also save some time by jumping straight back to the control from the crane unit, rather than moving the whole thing back towards the control room.

Segment 35: Separation

Nothing really to talk about here. This segment is brings the D6 area of the game to an end. Next we move on to the final levels.

Segment 36: Tower

The first part of this level is just a re-hashing of the battle from the first segment of the game.

After Miller saves you from certain death at the hands of a hungry demon, you make a break for the tower. The combat looks simple, but it's a real pain to take out the mutants quickly in order to keep Miller moving forward. The faster Miller moves forward, the faster you can complete the level. If you move to fast though, the game just goes to a scripted action and auto-kills you.

(Note: This was the only level in the game where I found a way to consistently get out-of-bounds. Unfortunately, it saves absolutely no time and is of no benefit.)

Segment 37: Top

I spent more time on this segment than any other in the game. I found a way to completely skip the scene where Miller gets attacked by the demon. This required super precise jumping.

I also found a way to skip the interior part of the tower where you are automatically put into slow motion and are required to listen to the words of the Dark Ones. This also required very precise jumping.

Basically, pulling off the jumps in this segment was, execution-wise, the most frustrating and difficult tech to pull off in the entire game. There are three very difficult jumps to pull off and messing up any of them required a new attempt. The clunky and random object collision (getting stuck on random ledges, objects, platforms, etc) caused endless frustration.

Segment 38: Ethereal

After how execution-heavy 'Top' was, blazing through this level was a breeze. Nothing fancy required here, just learning where you need to go and doing it as fast as possible.

Thanks for watching/reading!