Thought about getting back into TASing and gave this one a shot. It is as boring as grassini implied. So far I have only done part of the first level (up to about 31 seconds in his stream) but up to that point I have managed to save
~6.2 seconds.
145 frames were saved by going through the intro screens faster by hitting start.
Another 227 frames were in the actual first level. These frames were saved in 2 ways. First I found that if you hold A down your max walking speed is almost double what your speed is without it. Holding A you follow a pattern of 111 subpixels/frame, 112 subpixels/frame and 113 subpixels/frame. Without holding A the max speed you achieve is 63 subpixels/frame, 64 subpixels/frame and 65 subpixels per frame. What is stupid about this system is that hitting A causes you to jump so the only way to sprint is to jump and then hold A after you have hit your maximum height.
The other speed improvement was taking advantage of the pause damage glitch used in grassini's run. The glitch is that when you receive any damage your lose all of your horizontal speed and go through an animation that freezes your character for a few frames causing you have to accelerate back up to normal speed. With the glitch you can pause and unpause right as you are damaged to prevent the damage animation and not lose any horizontal momentum. Sadly this glitch does not work with fall damage as seen in the previous run, but if you line up your jump so that when you land you take damage from an enemy and not from the fall you can avoid the freeze in many other situations.
If anyone has any input on the run let me know. I can't guarantee I will actually finish this one but I'm giving it a shot.