I have no idea how they work, so I'm adding ClassicOne as a mod because looking at his speedrun history he does seem trustworthy.

This way at least one mod knows what's up

Thank you for that and I am more then happy to explain what happened in that run. The main glitch I found that lets you complete the level is a combination of Shop Storage and Death Abuse through the Pause Menu. I found that if you paused while jumping at certain points, the screen could become black with nothing on it. That is mostly the best time but you could do it as well on certain levels without the screen going but you have a better chance if the screen goes dark. Once you pause at that point, you would press the pause button again along with the jump button and if done right, it will cue the Level Complete Trigger. The important part is visiting the shop because after you do that, it locks you out of the pause menu because you are in a glitched state and going to the shop lets you access the pause menu and able to do the glitch moving forward. The only place it seems you can do it without going to the shop is the last World where it just seems to work for the most part. The important part too is to reset your lives since doing the glitch takes sometimes 1 life and other times leaves you with 0. That can be done by pausing the game and then pressing the attack button and it will reset the level and your lives. If anyone has any further questions or needs to know anything else about the glitches, feel free to get in contact with me.