So I got inspired by HeRMe (who beat my old 2008 run this year in 2015) to try this game again, and I got unexpectedly good results!
I want to thank him for his support back in 2008 and now again to plan and improve this run.

Like him, I am also running on casual difficulty now because I wanted to see how fast this game could be finished under any circumstances, like HeRMe did. But I did not only run the same route with more efficiency, I also found some more tricks and shortcuts I will try to explain in this commentary. My aim was to cut his 1:07 time down to under an hour, but in the end I even managed to cut down my old 2008 time in half.

Technical note:
This speedrun was run with vertical synchronization disabled to keep my graphics card busy and recorded with shadowplay in shadow mode to allow me to still play with high fps (150~220). Some tricks are not possible or harder when playing otherwise. This can also have some negative effects like not being able to get on a ladder or getting stuck in the ground.

Level 1: Arrival
There is not much possible here, because you only get time powers in level 2.
3:11:
I crawl at a 45° angle because this is ~25% faster than crawling forwards.

Level 2: Back again
Here I get my time powers, the first thing I do is some crazy impossible jump... I skip getting the shotgun, I will get it at level 5 again.
4:53: I wait for time-reverse to be enabled by the game and then launch myself, I will try to explain this:
We knew back in 2008 we could stand on a fallen down barrel and time-reverse ourselves up. HeRMe did a bigger jump while doing his level 2 with another route by accident, so I tried to reproduce this. I found out that if you time-reverse while standing on some physical object and mash jump you sometimes get a boost in that direction. Then by accident I noticed that I could get a much bigger boost by playing on a friends computer that had weaker hardware. So after some research I found out that the physics engine tends to be weird and give such big boosts when the graphics card is busy. I was able to reproduce this behaviour by playing the entire game with vertical synchronization off, so the game was running with ~200fps and the graphics card was busy. 5:03: I get "stuck" in an out of bounds clip. In this game you can still walk reaaaaal slow in them and are also sinking slowly. I walk out of the clip and fall to the ground (After exiting oob fall damage for the current fall is somehow disabled). After that I walk through that oob clip. When you enter oob while walking, you can still walk (while slowly sinking), but if you fly in it you get "stuck", like before. 5:13 I walk towards the end of the level through an area that is usually not reachable in the game. I also try to use time-slow as much as possible while walking, because walking is ~9% faster this way.

Level 3: New blood
7:09: By nade-jumping over the first guy I don't unlock time-reverse for this level, which was needed for HeRMe's technique to jump over the fence, but I managed to do that with a double grenade jump. 7:26: I get hurt on purpose, because I can heal myself using time-stop when I have < 25% health. HeRMe discovered this, but did not really exploit it through his entire run. 7:33: I use two karbine grenades to jump over the fence with the help of the dumpster. This is made possible by using casual mode, being able to detonate the grenade just on releasing RMB and letting it explode not directly under you because it would still kill you.

Level 4: Infiltration
9:09: I jump over the wall like HeRMe and skip the majority of the level, but I do it with a double nade jump again and not by using time-reverse with an object.

Level 5: Ground floor
I pick up my shotgun here, the tricks are self explanatory.

Level 6: Heist
This is using the same route HeRMe uses, but more efficient.
12:05: At this point everyone has spawned that I need to kill. Only then will the door be enabled.

Level 7: Getaway
13:25: I do a couple of jumps here. I get intentionally hurt so after the jump my health is low enough to time-stop-heal again. 14:00: This battle is heavily optimized, I don't need to kill the jetpack soldiers for the cutscene to trigger. At 14:07 I stop time-slowing because there is also a delay before the cutscene can trigger after I hit the switch.

Level 8: Disputed airspace
This level makes you want to have a time-fast-forward power... It is the equivalent of an autoscroller level, I don't use any time powers, so this is a "perfect" level. I also lose karbine grenades and normal grenades for some reason, this is always the case.

Level 9: Better late...
I shoot the quad because I need a wheel as a physical object to boost myself up the mountain. From there I just walk oob towards the level trigger.

Level 10: Point of impact
I use a barrel again to time-reverse-boost myself to "fly" through the level. I have to activate the train or else the level trigger is still disabled.

Level 11: Liberation
Since this is also indoors I can't do crazy jumps or go oob. I mostly just walk through which is easier with casual difficulty and time-stop-healing.

Level 12: Road trip
The fastest level in this speedrun, I just fly towards the level trigger right away. Level triggers often have infinite height, so it even triggers when I am high above the area. It's funny, I even skip the cutscene that is "at the start of the level", but with a small delay that is too long for me.
Game: "Here, take this vehicle"
Me: "Thanks." *Shoots it and flies away*

Level 13: Forced entry
Unfortunately there are no physical objects in this level to use for the longest time, so the start is pretty casual.
25:35: I double-nade-jump over the fence to avoid the trigger on the right, making me stand there for several seconds and hearing a speech.

Level 14: Test labs
28:01: I boost myself to the control center and not to the fan in the center, because I actually have to activate it first. There is space outside the fan tower, but I cannot reach a level trigger or something useful from outside the fan area. 28:25: I double-nade-jump over the railing (necessary because there is a bigger clip wall) and land on a pipe, skipping the ladder, a little fight and jumping around a bit. I survive this because I land on a slight angle on the "round" pipe, a litte to the left or right and I would have died.

Level 15: Factory recall
29:14: I do a complicated grenade+crossbow boost because I only have 1 karbine grenade left and that would not be enough. The crossbow also gives a boost, though not as big as with a normal (karbine-) grenade. 29:20: I do a little oldschool surfing there. It seems this is only possible on edges that were thought to be inaccessible. Later in this level and following level there are better opportunities for this. 29:33: I exploit the healing effect when time-stopping with <25% health. After the two jumps I only heal enough so I can heal after the next jump again to survive the last jump. 30:10: More surfing action. Also the wall textures get a weird shader, this may be caused by the lack of tech support for this game and the fact I always get driver warnings at the start of the game. 30:22: I survive this because I half-land on the angled lamp.

Level 16: Some assembly required
31:15: This jump is lethal. Though the game autosaves right before I land and when I load from that save to start a new segment the lethal velocity is removed. 31:28: I can't walk too far here, if I walk past the part where I activate time-reverse the game would disable time-reverse for some reason. After the jump I wait a bit because I need time powers for the next level and can't wait there.

Level 17: Sabotage
I hurry at the beginning to get to the first rideable transport pod, this is only doable because I saved up some time powers from the previous level.
31:54: This surfing part is not possible with vsync enabled in my experience, you just fall down like the logical thing that would happen. 32:02: I wait for a bit to recharge time power to use time-reverse longer. (Though it is counterintuitive that you can reverse more time than you wait for, but it works) 32:14: This looks a bit derpy, but it is also tricky. The transport belt is moving in a direction, I am exiting the pod while using time-reverse, stop it, the belt changes direction, the pod pushes me away a bit and the world plus the input lag can still be a bit different, so I kind of dance there for a moment. 32:53: I hurt myself on purpose to time-stop-heal again. Then I skip another part of the level like in HeRMe's run, but with better jumps in this room.

Level 18: Exeunt
"Just keep going up as fast as you can."
This jump is a bit tricky, because it is easy to jump waaaayyy too high, which still makes the level completable, but it is bad for the time.
33:55: The gate I open should only be opened from the inside, good thing some dev made the outer button also usable. 34:00: My suit AI voice does say that I should hurry, but only because a normal player would not reach that ship without time powers. I still have to wait for the ship to be raised before the end level cutscene triggers, so I just walk.

Level 19: Drive by
35:34: I fly towards the level trigger that is inside the vent.

Level 20: Gate crashers
We already had this route back in 2008, I just optimized it a bit.

Level 21: The wind tunnel
36:24: The soldier dies in the cutscene by being sucked up in the wind tunnel. However, if I cancel the cutscene even before he leaves the room, his weapon is still left here. 36:33: I have to wait for a bit because I can only rewind to the earliest point in time where time-reverse was enabled, that is the point where the guy said "bastard". I need enough time to reverse to make it across the room. 36:54: I time-reverse-boost myself up to the ceiling and fly further to the button I need to press to deactivate the wind tunnel and trigger some more scripted scenes to progress. This jump saves some bigger fights, HeRMe did it before, but only jumped straight up.

Level 22: Repo men
I can't leave the train at the start, I leave it as soon as possible. Time-reversing was also disabled for some reason, so after leaving I have to wait for a bit for it to be re-enabled again.
38:42: Since there is also no falling damage after getting boosted by physic objects for some reason, I can skip the entire level and just fly towards the end elevator. I can't jump directly on top of the end room through oob, because I get completely stuck in the ceiling then.

Level 23: En route
This level starts with an autoscrolling mode again. Not using time powers and just shooting the helis is the fastest method. I can even miss some shots, that does not change anything about the time when the ship docks. Also I lose my karbine grenades and normal grenades again for some reason, like the game does when entering a zep level.
41:10: I tried to just get to the exit of this room, but I didn't find a way to survive this, even with frequent time-stop-healing.

Level 24: Consequences
I lose all my weapons at the start, so no fancy jumps here. When I find some I am indoors, but doing jumps in this level would still not be useful since it relies heavily on script triggers. I could not finish the boss in the final part when I miss these. There are no fancy tricks in this level, I just do it really efficient.
43:22: We used to do this battle in waves and hide in the right corner to avoid artillery, but if you are fast enough it is possible to finish it before that. You need to use that exact weapon I use to destroy the crystals and I must do this from this area or the boss does not move to the final area. I shoot the first 2 crystals at approximately the same time because the boss enters an angry state when one gets destroyed and moves too much. 44:16: Killing these guys is not only because of boredom, the boss seems to move earlier when these guys are dead. 44:36: We used to shoot everything we have at the crystal at this point, but I found out that it is invincible until a certain point later and then only needs 3 shots, whoops. Run time stops when the crystal explodes.

That's it! I hope you enjoyed the speedrun, it was fun to do!