Really good work! It was cool to see you stack all those enemy combos, and make use of the partner's ability while attacking with Aang/Zuko (especially Dragon Breath!). You thought of plenty of surprising ways to use two attacks at once to save time.
Is it possible, by waiting a few frames or entering different input, to make Azula throw more small fireballs instead of the huge ones? Or does she follow that same pattern every time?
Also, in Level 2, around frame 15000, you held onto that charged fireball for a long time. Couldn't you have used it to help fill that red crystal or defeat the firs two enemies in the next room, and then started charging another one?
Sometimes you stand still and wait for enemies to get into a certain position before attacking. You can skip this wait sometimes by changing your own character's position to make them move differently, into a position where they can get hit faster.
I used to wonder how everyone found such cool glitches too. Basically, just play around with the game, while recording a movie so you have a record of whatever you find. Try things that the developers didn't expect you to do, and you just might find something useful. One common trick is making two things happen at once, which can lead to things like
midair jumps and
cutscene skips.
Yes, frame advance is essential to making your TAS the fastest it can be, almost as important as savestates.