3-3 Glitch
What It Is
The 3-3 map corruption trick allows you to skip the submarine section by doing the tongue glitch to rearrange the objects in the level to allow you to reach the second middle-ring from the second screen and you need either a POW block or a big egg to do it. Big eggs are recommended, as there is no known way to consistently get a POW block, but there are strats for bringing a big egg from 2-7 into 3-3.
This trick used to save around 40 seconds in the Any% Warps, No Null Egg category but since resetting the console between worlds was allowed back in May 2017, via a vote in the Yoshi discord server, the trick now saves around 20 seconds. A comparison video can be seen here.
Keep in mind, this trick is banned in Any% Warpless.
How To Do It
First you'll need to Baxter a big egg in 2-7 and then again in 3-1 and 3-2.
For 2-8: Simply be aiming the big egg before the boss falls off. To be safe, aim the egg when you give the boss the final push off of the edge. [1]
Once you reach 3-3 with the big egg, go to the 2nd screen, grab an enemy, throw the big egg into the air and spit out the enemy right before the big egg lands. This will activate the tongue glitch. Next, go to where the shy guys are on the red bridge, tongue and get hit when Yoshi's tongue is fully extended. This will activate the second phase of the tongue glitch and turn Yoshi and Baby Mario invisible as a result. Reclaim Baby Mario and do a full jump followed by 3 flutters to enter the helicopter bubble. Once you transform into the helicopter, you'll notice that the map has become corrupted. Fly to the right and enter the middle-ring then hold down to die. Upon respawning, you will have successfully skipped the submarine room.
Here is a demonstration of the whole trick. Here is alternative method to do a fast big egg Baxter.
Tutorial
The following tutorial explains how to carry the big egg from 2-7 to 3-3 and it also explains the Tongue Glitch.
Big Egg Baxter Visual Cues
If you do "slow baxters" (Where you visually confirm the egg position first) the following picture will help you to know where you have to put the egg so the next Yoshi can pick it up or where it will fail. For 2-7 it's fairly easy since the camera isn't locked, but for 3-1 and 3-2 the camera will be locked stupidly, but it can be somewhat worked around if you know where to put the glitched out big egg. Reminder that the big egg despawn if too far off-screen.