Army of Two: the 40th Day - retry glitch in Chapter 1
This is a pretty versatile and unique trick that has the power to glitch up a checkpoint retry, and it even creates some effects that are useful in a speedrun!
Here are all the different results from Chapter 1, and I'll probably look into later Chapters too sooner or later since this is pretty fun to mess around with.
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To do this glitch, you have to buffer a shop menu over a retry by timing the shop prompt correctly. This causes the weapon shop to open up as the first thing after retry.
After you close the shop menu, the game loads a bit and then the checkpoint seems to begin like normal. But you may notice that it does so with a strange delay, with you having several seconds to move around before the fade-in signifying the actual start of the checkpoint kicks in. Yes, you are in fact starting the checkpoint too early because of the weapon shop; before the game has finished loading things right.
You can make the glitch effect indefinite instead of lasting just a few seconds if you quickly open weapon shop again before the level starts properly. This way (after closing shop again), the checkpoint begins without its first triggers activating at all. The results vary depending on checkpoint, of course.
The glitch only affects the first triggers of the level. If you play onward, things will typically work normally from there on.
Since you have to retry and visit the shop twice while starting this glitch, it's pretty costly to set up in a speedrun. At the minimum it takes around 15-20 seconds. If a checkpoint begins from an unskippable cutscene which you have to watch before you can access the shop and retry, then at the very least it will be very wasteful and probably not worth it... but even this can vary depending on the level, I guess.
The only limitation to this glitch is that it can't be started in checkpoints where the shop menu can't be opened.
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0:00 - Chapter 1-4. I start from this Chapter because the footage is slow-paced enough to explain the workings of the glitch.
Since you skip the first triggers of the checkpoint, you never see the cutscene where large parts of the city explode. So, the city stays intact and countless of lives are saved! A door behind you also stays open, allowing you to see a glimpse of the out of bounds area.
(Not on the vid: Chapter 1-1. Can't make the glitch effect indefinite there.)
1:34 - Chapter 1-2. The elevator doors never open and the heroes are stuck inside.
(Not on the vid: Chapter 1-3. Things seem to work like normal.)
2:03 - Chapter 1-5. The cutscene with the mercenaries doesn't activate nor will any enemies spawn. You can see some abandoned weapons left on the ground, but the bad guys themselves are nowhere to be found.
While this is a fight skip, doing this is probably not worth it in a speedrun because the checkpoint starts from an unskippable cutscene.
(Not on the vid: Chapter 1-6. Things seem to work like normal.)
2:43 - Chapter 1-7. A massive fight skip! None of the enemies in the area spawn, allowing you to just run past without any worries. This is most likely worth it in a speedrun.
3:53 - Chapter 1-8. Hostage situation skip. No enemies or civilians spawn, which makes the tutorial cutscene look pretty humorous. Doing this probably wouldn't save time in a speedrun.
(Not on the vid: Chapter 1-9. Things seem to work like normal.)
4:40 - Chapter 1-10. Slight event glitch. You start from the control room beyond the large gate with the gate still closed. Nothing happens until you tell your partner to proceed, after which he finally opens the gate using the console which lacks a prompt. Then enemies start flooding in and the level continues on from there like normal.