Well I wasn't going to improve the file with the known improvement that I mentioned of stage 3-1. But I started fiddling with the earlier stages and right away I found around 6 frames of improvement. I don't expect any major changes, but I'm going to at least update the file with these and see how it goes. Will keep it updated as I find things, and hopefully it shouldn't take me too long to finish, if things go smoothly.
Update #1 Finished World 1
52 67 frames faster. This world was finished fast because none of the enemies are RNG based, so the levels sync up nicely. That's not going to be the case with World 3. I wasn't expecting to find this much improvement to the first world, so I'm definitely going to update with a few file, hopefully within a couple of days.
Update #2 Finished World 2. Total savings is 125 so far.
Update #3 So, just entered the world 3 boss fight at 199 frames saved. Now the main annoyance of this run: The boss's arms can move in different patterns, despite having the same exact input. I still haven't quite determined what this is based off of, as improving the previous level multiple times still yields the same outcome. It's different from the time I fought him in the file above, as many of my shots miss his arms immediately. Now I don't think it will be too much time difference if I adjust all of my shots, but it would really benefit from knowing how to manipulate him if possible. I assume there's some large frame rule that changes his actions every set number of frames. I don't have anything to base this on, but it's the only way I can explain it.
Update #4 Worked out the world 3 boss, total time saved is 218. I actually completed the boss even faster this time by better positioning despite the different pattern. The only thing that really matters is his right arm, it needs to die as close to the central body as possible so that I can immediately fire onto it. Hopefully I'll be done with the last world by tomorrow.
Final update: Finished. Here it is, 301 frames faster:
http://tasvideos.org/userfiles/info/49537548110145992
Anyway, with that being said almost any small improvement before stage 7 would probably make this trick possible. Which means I come to my other idea.
I was wondering if it were somehow possible to get those throws to land on the garbage boss tiles in stage 4 and still have ronald land on the boss's existing mouth instead of falling all the way to the floor. It seems we miss a phase of boss tiles existing while we're trying to get back in position. Again, no proof just theories.
Also, I'm pretty sure some of the other submissions had a better Hamburglar fight near the end of the game: attacking the ground so that the apple's timer runs out sooner than it would by attacking him directly at the start. I didn't actually compare times, just observations.
In fact I believe stage 1 can even be improved in theory. In my head, we should have less frames with no apple boost than we do and also we should be flying directly into the boss to get as early hit as possible in. I don't know if any setup would allow for that; but it makes sense in my head.
That's about all I have for the moment, I might update this post if anything else comes to mind.
[edit]: I've already found several small improvements that were inspired by taking a look at these maps, so they are actually coming in handy.