Okay, first off, I'd like to thank the following people:

Mkt2015: For mentioning this game as a potential speedrun. Also for advice, particularly about move purchases.
bsidwell: For general advice on the game.
KillerMiller: Big piece of advice for dealing with the Orochi Hellbeast in segment 6, as well as general advice and making the (now proven) claim that sub-1:30 was possible.
Tetsuo9999: A good portion of his advice focused on the battles in the final segment, specifically Shang Tsung and Shao Kahn.
LASVEGAS: For prodding me into submitting this - I was hesitant because of a number of miscellaneous issues - some technical, some emotional, not all involving me.
LazyKenny: He prodded me into skipping the life upgrade from Kano, which would have otherwise tacked on an extra four or five minutes before the final battles.
Radix: Not only for the site, but for bearing with me while I tried to explain the game to him before I submitted.

If I missed anyone, I apologize - these are the ones I remember. Honestly, I've taken more advice during this run than during any previous run I've completed.

First off, my segmenting. Generally I save right before difficult parts or at the start of new areas, unless there are other complicating matters. The main reason is that when you use a save point, your health is restored to full.

Second, the deal with the game's cutscenes. After you've watched them once (in ANY playthrough), you can skip them after a certain duration has played - I think it's about 5% of the cutscene or some percentage like that. A weird system, but it guarantees that someone who hasn't played the game and is watching KNOWS you skipped a cutscene.

Next, move purchases. I don't need to buy every move in the game, and besides, that takes too much fighting to accomplish. The fireball moves are the single most important move for Liu Kang to pick up in a speedrun. The combo moves simply allow for faster damage dealing, and the extra uppercut is best used for large bosses (Goro and Kintaro come to mind). I considered the bicycle kick (after several people advised it), but I could never get the move to work consistently enough, even by my standards (which, when it comes to doing moves consistently, are pretty low), so I removed it from consideration.

Finally, segment-by-segment commentary (I recommend watching the run as you read it or reading it after watching):

Segment 1:
-Throwing enemies into the fire is, to my knowledge, the single fastest way to deal with them. And since I have no need for much experience this early, I take advantage of that fact.
-Liu Kang's flying kick allows for only minor speed boosts, but since I don't yet have the Long Jump that's the best means of going fast.
-The fatality meter, to my knowledge, is based on how many hits you inflict, not how much damage. Therefore, I rely on just hitting opponents instead of high-damage moves.
-Liu Kang has a much easier time aiming his throws into low places than Kung Lao does.

Segment 2:
-I need that sword to make the first boss go fast - that's why I make sure to start the segment with grabbing it.
-The 'coin' with the Long Jump ability doesn't appear until the cutscene I skipped would have ended normally - I just skip the cutscene on principle. The most time I could have saved by being in the right spot at the right time is probably half a second, so my precision is pretty good.
-Speaking of precision, it's not always easy to make that first required Long Jump on the first try. Or the second (I mean the second jump, but 'on the second try' also works).
-I kept the sword because weapons in this game are completely unblockable - although you can't block when you have one. A decent tradeoff, as I demonstrate at the final bridge. Probably could have waited during the 'lift' to cut that second guard one final time in midair to save time, now that I look at it again two months after I completed the run, but oh well.
-I got a little overzealous trying to skip a cutscene after knocking down the second set of spiked balls, which should explain the pause there.
-I also was a little imprecise with my jumps over the spiked pit.... at least spiked pits aren't lethal like they are in other games.
-Bit of a brain fart after the first time I had to defend Johnny Cage... cost me maybe one second at most.
-I grab this health upgrade because it costs very little time and allows me to survive more easily.
-My secret to Test Your Might is this - I use the index and middle fingers of my right hand for rapidly hitting the buttons, and I use my left hand to hit the shoulder button when the meter is at an adequate level.
-I hit that Tarkata near the last wheel so that he wouldn't get in my way when I went for it.
-Looking back on this now, that was VERY bad timing to buy a move. I should have waited until I had plenty of room.

Segment 3:
-No, I DON'T know how that happened at the very start.
-I've messed up that Long Jump at the Portal several times in the past.
-Not the optimum way of dealing with the first puzzle in the Monastery, but it was the best I could do.
-Very funny how I only have to glance the enemy in order to pull off a finishing move. Works for me, actually.
-The part climbing up here is one demonstration of why Liu Kang is the superior character for a single-player run. From my testing, Kung Lao would have to throw the enemy to remove them fast, whereas Liu Kang can use a much faster flying kick. Or if Liu Kang HAS to throw, he can do it from farther away.
-That pillar is nearly impossible to jump over without taking damage. This being near the end of the segment, I accept something minor such as this.

Segment 4:
-Yes, I know I'm acting cheap against Kitana. It's a minor boss fight - what do you expect?
-In the first phase of the REAL boss fight, only Kitana needs to be struck down - it in fact wastes time if you drop Mileena or Jade's health too far. I wind up dropping Mileena's health too far because she wouldn't stop trying to free Kitana - serves me right for trying to save the girl (even though you HAVE to save Kitana).
-In the second phase, as soon as I drop the health of either Mileena or Jade to the point where they're trapped, I go after the switch near them in order to guarantee a faster health drop. It doesn't matter which one you defeat first, because you'll have to weaken both of them to execute the Fatality. While we're on that subject, every boss has a very specific Fatality you must perform in order to finish them. And unlike the fighting games, you HAVE to finish them with Fatalities.
-I grab experience here because I feel it is somewhat necessary in order to get good moves later.
-Again Liu Kang shows his superior skill, for he has an easier time hitting those dark statues. He also has an easier time knocking enemies off of cliffs.
-Now, supposedly there was a rumor about being able to feed the Living Forest's trees in Mortal Kombat 2. While it can't be done in that game, it HAS to be done here - plus the first one is a great way to get rid of enemies that MUST be killed to progress.
-I was actually screwing around with the uppercuts when I inadvertently impaled the third Putrid Corpse enemy on those hanging spikes.
-Wow, I felt REALLY stupid when that tree grabbed me. That, or really panicky, I don't know which.
-Brothers of Shadow are the second hardest enemy in the game as far as I can tell (the first hardest being Shao Kahn himself), because of their means of attack. A Fatality or Multality is the single best way to deal with them, but it takes luck to hit them all at once with a Multality like I did here.
-I don't want to say the hit detection of the snakes sucks outright, but it's pretty bad, as one of them is glad to demonstrate.

Segment 5:
-I think this is the only time I've gotten every one of those moving statues on the first pass. And I have NEVER been able to do it with Kung Lao - only Liu Kang. I don't get it.
-The Brutality takes too long to build up for common usage, but there is one place I really NEED it. I'll get to that later.
-The giant serpent is the most aggravating miniboss the game has to offer a speedrunner - I would dare say this is more aggravating (though not as difficult once you know the pattern) than Shao Kahn. See, one mistake and you have to climb back up and lose lots of time.
-I buy the next part of the fireball sequence, as well as a combination move, here. Watch as I immediately put the combo move to use. I use it some more later, but for now the combo and my fighting skills prevent Reptile from ever using his hated 'scattering forceballs' attack (he will only use it in the first half of the fight). However, he gets plenty of revenge in the second half before I finally put him down.
-Considering the look of the walls that you can climb, why does it take this long to be able to do it?
-Yep, you can jump up the walls like this.
-Normally I would continue onward rather than saving here, but the next part is absolute hell, and I don't want to have to deal with that giant serpent again.

Segment 6:
-This is the one segment I absolutely HATED doing. It is also the segment that prevented me from doing a Kung Lao run.
-I take this route through the Soul Tombs because, to use a strategy that was suggested by KillerMiller, I need to build up a Brutality before I reach the Hellbeast. This is the easiest way for me to do it.
-The Tarkata are the only enemies I know of in this game that work this well in groups.
-I would almost classify the incident where I supposedly misjump and land in the spikes an instance of 'takes damage to save time' - the problem is that it was not intended.
-The second part of the fan room makes me think the people at Midway are sick and twisted beyond belief.
-I hate jumping sections that are partially in 3D rather than fully 3D or 2D rendered in 3D.
-What the heck did the guys near the statue with the sword DO to deserve being used as door weights?
-The sword can't damage the containment part of the Soul Tombs, which is why I ditch it so fast after cutting down the weights. Speaking of that room, I'd like to point out there is a certain amount of 'tunnel vision' required in a speedrun, where you act like anything except what you need to destroy doesn't exist. I think I demonstrate this quite nicely.
-I'm not the kind of person to split an area in half unless it's really necessary, so I hold off on saving.
-The outside area is probably the most difficult 'Test Your Might' portion in the game, because you not only need good button-mashing skills, you have to know WHEN to pull the lever. This is why I wait to initiate the 'Test Your Might' sequences. Getting all three in the first try the way I did is rare. By the way, why do those gates only stay down when someone's smashed under them?
-Any of you who has had trouble with the Hellbeast before should watch as I obliterate him in less than 10 seconds with the fire attack from the Brutality. That's the high point of the segment, as demonstrated when returning as I get hit by fire TWICE. I don't want to fight the Hellbeast again, so I save it as soon as I can.

Segment 7:
-Normally, most bosses counter after about five hits. However, if you time your moves properly, you can prevent counterattacks and keep them pinned until an event hits.
-I make it easier on myself by getting rid of the two flaming monks right away. You can only do this with projectiles, so Liu Kang has more leeway here.
-Speaking of projectiles, Liu Kang has a big advantage in the third part of this fight since he can throw more than one at a time (with the right moves).
-Is Baraka's skull really that hollow? And if it is, how did he ever manage to become a leader of the Tarkata?
-There is no better time to return and get that Wall Run move than now - getting it earlier is a waste of time to my knowledge. The Wall Run and Wall Jump have limited use, which is a good thing for me, because I didn't buy this game to act like the Prince of Persia (see those runs for more details on what I mean) - I bought it for the fighting.
-I officially buy the last of the fireball sequence here, in order to make future fights easier.
-I cannot stand fighting the Elemental Knights. Let's just leave it at that.
-In retrospect, I probably should have gone for that Life Upgrade - it was not that far out of the way and might have made the last few fights much easier.

Segment 8:
-Sub-Zero's killed me a number of times before, which is why I start the segment with him. This is the closest I've come to total ownage of any boss, as far as I can tell. By the way, the cutscene I skip here shows where versions of Sub-Zero from Mortal Kombat 3 onward got that scar of his, but judging from what is seen of the cutscene, I don't think it takes much imagination.
-One of my worse handlings of the grinder room, in my opinion. Also further proof that Midway's developers are sick and twisted.
-Kicking those two mercs into the pit right away saves me some serious hassle when Sub-Zero goes to freeze the wall.

Segment 9:
-Goro is the least bothersome of the oversized bosses in this game. However, I wished I had built up enough experience to get a second uppercut here - it might have sped things up. I generally think Goro is EASIER to fight when he breaks out the oversized pillar, but I got a little too reckless here and lost a lot of health.
-Dammit Cage, quit killstealing! That was MY victory!
-By the way, I'm pretty sure that was a kick all the way THROUGH Goro's waist. If it's not, well, that's a pretty evil way to get killed.
-The Dead Pool is where I'm regretting that lost health.
-I save at the start of the Netherrealm because Scorpion is the longest individual boss battle in the game.

Segment 10:
-Once again I demonstrate the ability to prevent bosses from countering after five or so hits.
-Does the Netherrealm have a band or orchestra at all? Because I think Scorpion would be an excellent conductor. Just watch him.
-The spear is built into Scorpion's hand, in case you didn't know. This is why it's so easy for him to reel in enemies that are speared. Similarly, that's also why it's so easy to pull him in like this.
-I don't even give Scorpion time to put his mask back on after a botched fire breath attempt. Although I kinda see why he wears one...
-This is what I was saying about Scorpion being a long boss battle. He just won't give up. His spear is the most worrisome part of the second fight. By the way, I think the second Fatality input for Scorpion is simply the first with every direction reversed.
-To my knowledge, that 'thumbs up' is a Terminator reference.
-I take care of this wheel before saving so I don't have to backtrack later.

Segment 11:
-I absolutely hate the room with the Hellbeast. At least you don't have to fight him.
-Like how I crushed one guy between the mallets? That gets you a secret, but I've already gotten that secret before.
-All this trouble for an axe? Doesn't Outworld have any decent armories or anything?
-I don't want to backtrack, so I save the second wheel for after I get the axe.
-That break-apart method doesn't make much sense considering where I smacked the crystal, but oh well.
-Great timing on the Multality, isn't it? That's the last one you'll see for this run.

Segment 12:
-This segment is all boss fights. I would have gone for Kano here to get a better life boost in the middle of the battle, but it proved to be a time-waster.
-That slowdown in the Shang Tsung fight seems to be a bug in the game's code, as I'm not the only one who's experienced it. By the way, it's one of the better fights I've had against him.
-My unorthodox strategy against Kintaro is necessary to conserve health - I need sufficient health to beat Shao Kahn, but I still need to beat him fast since this is a speedrun. Abusing the rolling technique is the result for the first half, but then I discovered that Kintaro's counterattack, if he does it at the right moment, actually hurts him pretty badly. Since I had a lot of health, I decided that would finish him quickly.
-If you wonder why I jump so much against Shao Kahn, it's because he'll try to attack you in midair if you try to jump at all. I can abuse this to get him away from me, since I'm too far down for him to strike.
-I think it was Tetsuo9999 who convinced me that Kintaro's head was indeed the fastest means of dealing damage against Shao Kahn. The problem is hitting him with it - the hitbox for knocking Shao Kahn off his feet (or just hitting him half the time) is annoyingly small beyond reason. There's some evidence of it in the first half of the fight, but it's clearer in the second half.
-I stay very far away because Shao Kahn's attacks hurt horribly. This is especially true for the hammer swing attack - if I get hit by any part of that I may as well restart because I've lost too much health to continue the fight.
-See that guy with the pale skin at the end of the final cutscene? That is Quan Chi (who also shows up in MK Mythologies and a few others), and let's just say he's not a good guy.

Well, that's about all from me. Enjoy the run.