This is a TAS of FDS Super Mario Bros. 2, specifically of the letter worlds. You can play the secret letter worlds after getting 8 stars on the title screen, and you can access them by pressing A+Start on the controller at the title screen--as such, getting 8 stars is required before being able to play the movie, which means this TAS starts with an unclean SRAM state. This means a verification movie is required, which can be found here: https://tasvideos.org/UserFiles/Info/638008645247617084
The linked movie gets the required SRAM state this TAS uses to start directly in world A.
During the creation of this TAS, I investigated the possibility of big Mario being faster than small, as big Mario can perform crouch clips in B-4 and D-4, and bullet bill glitch in D-3 to save a significant amount of the time lost getting the mushroom. However, the small Mario TAS ended up being 26 frames faster, so I went with that route instead.
I also investigated timesave in D-4, as this TAS loses many frames throughout the level in order to get a good Bowser pattern in the last room. However, I couldn't manipulate Bowser's pattern, or go fast enough to get another good pattern, so unfortunately, unless a new framerule save is found, this D-4 is as good as I could get. However, this D-4 is still 4 frames faster than the D-4 in my old TAS, so it is still an improvement overall.
Finishes D-4 from A-1
Aims for fastest time
Flagpole Glitch (FPG): Used in B-1, B-2, B-3, D-2, and D-3. By clipping into the wall in a 0.5 pixel window, you can touch the flagpole lower than intended. This activates a normally completely unused bit of code that causes the flag-lowering routine to be skipped, allowing Mario to finish any levels with a flagpole 21 frames faster than is otherwise possible (in most cases--see the FFPG section or SMB1 8-3 for exceptions).
Full Flagpole Glitch (FFPG): Used in A-1 and D-1. By touching the flagpole even lower than is possible with FPG--either by clipping in the ground as seen in this TAS, or by using an enemy bounce like in 8-2 of SMB1--Mario is too low to snap on top of the flagpole block, causing him to be ejected out to the left instead. This causes the timer countdown to begin earlier than is otherwise possible, which can save a large amount of time.
Wall Clip: Used in A-1, A-2, B-1, B-2, B-3, B-4, D-1, D-2, D-3, and D-4. By pressing left within a 1 pixel positioning window, Mario can be pulled into a block, rather than be pushed out of it as is normal. The amount of airtime Mario has before landing inside the wall will affect how far he goes inside, as the longer Mario is in the air, the farther to the right he will be pulled, which is important due to the fact that the moment Mario lands, if he isn't fully clipped into the wall, he will be pushed to the left. This effect is only used to get FPG in B-1, B-2, B-3, D-2, and D-3--however in A-1, A-2, B-4, D-1, and D-4 it is used to greater effect. In A-1 and A-2, Mario jumps barely too low to get on top of the block he clips into, which gives him just enough airtime to fully clip into the corner of the block with precise enough positioning. In B-4, D-1 (with help from the wind), and D-4, Mario doesn't have enough airtime to fully clip into the walls, however with a few extra jumps, is still able to fully clip inside.
Long Firebar Skip: Used in D-4. Due to the fact that firebars always rotate a fixed amount every ~6 frames along their length, the tips of firebars travel more distance than the center. With a long enough firebar, and precise enough positioning and timing, Mario can be on one side of the firebar, barely not touching it. Then, on the next frame, the firebar rotates, and Mario moves just enough that he's on the other side of the firebar, without touching it at all.
Here, I lower the platform in front of the flagpole enough to clip into the ground, which allows me to perform a full flagpole glitch, skipping the flag-lowering and walking to the castle cutscenes.
In A-2, I use a corner clip to enter the warpzone faster than otherwise possible. Unlike 1-2, there are actually three ways of entering the warpzone, you can ride a rising platform, perform a walljump near the beginning to get up top early, and then you can use the corner clip seen in this TAS, which saves 3 framerules over the walljump. Bruhmoment helped save the 2 frames necessary to make the next framerule, which saves 21 frames over the previous TAS.
Nothing special really, just a fast acceleration and flagpole glitch, though I tried my best to make it entertaining.
A water level! I perform an underwater fast acceleration at the start, something that is only possible using L+R, and unlike in SMB1 there are actually sections where you need precise swimming and slowdowns.
Nothing special either. This level is actually where I performed the mushroom grab in the big Mario TAS, as the first mushroom can be grabbed very quickly.
The first castle level, though we never get to meet the fake Bowser it contains. I perform a wall clip partway through the level, to skip having to ride the platform below.
In this level, I abuse wind mechanics to clip into the floor, allowing me to perform the second full flagpole glitch of the run.
Nothing special, though I do show off a glitch at the end, where if you jump on the last frame Mario is on the spring, he performs a normal jump instead of a spring jump.
Some cool enemy kills near the end, but other than that, not much of note.
In the first room, I abuse firebar mechanics to allow Mario to pass through the long firebar in the first room. In the second room, I have to slow down by 2 subpixels near the end to avoid being killed by the piranha plant. And in the fourth and final room, I have to clip through a wall to skip having to wait for the podoboo near Bowser to fall back down. I also have to avoid getting a backwards-moving Bowser, which in D-4 is always an impossible pattern without slowing down significantly.
: Looks good. Accepting as the warps run for the A-D level set.