I'm doing a TAS of this (my first, actually) and I've got a couple observations.
1. Jump-kicking the weaker Putties definitely seems quicker, but when you're not in Ranger form, the hit causes some loss of momentum, so it's best to hit as late in the jump as possible
2. When you ARE in Ranger form, you can hold back when jump-kicking and you'll backflip off the enemy when you hit. This is a tremendous time-saver, especially when there are enemies coming from both sides. I also use this to smash the Stage 1 boss's face in instead of repeatedly positioning to combo him. (Except for his final form, because a combo is all it takes to finish him.) (I finished that stage at about 16,000 frames.)
3a. I'm not quite sure how to manipulate luck to get the Stage 2 boss to appear where you want him to. I'm about 80% sure it's to do with where you're standing and what direction you're facing, though.
3b. Once he starts flickering around the screen, it is indeed a good idea to Bomb him. He flickers 23 times before becoming solid, and the bomb will go off perfectly if you fire it the 6th time. It does take a few more attacks before it'll kill him, though.
Here's what I have so far. Some critique would be nice.
http://fast.filespace.org/Keita-chan/Mighty_Morphin_Power_Rangers__U_.zmv
Yes, I know SNES9X is the emu of choice here, but I cannot stand it. I used ZSNES 1.51 for this.
(The movie desyncs sometime in Stage 2, don't quite remember where, only that it was before the boss. I think this is related to use of rewind and state-load.)