Are we attempting to do a communal breakdown of Rainbow times? I've got some I'm pleased with, and would be perfectly happy giving strategies.
Remix I-2: 0:21.9 (This one's pretty luck-based. Eventually you'll get a barrel pattern that doesn't kill you on any of the necessary ladders. Just climb up all of the most immediate ladders and jump over any barrels that are coming at you.)
Remix I-7: 0:12.3 (This one took me several tries. The trick is to upend the two most immediate shellcreepers on the (stage) right, and then when going up to kick them, upend the one immediately above you. If you can do this quickly enough, when you kick that one, the last will go into rage-mode and you should be able to upend it by dropping down both platforms before it hits the ground.)
Remix I-12: 0:18.5 (This one is really all above just taking them down as fast as possible. Don't let any get to the bottom and you'll be fine. Memorize their emergence pattern.)
Remix I-14: 0:21.5 (This one is again, luck-based. A good pattern will get you it without too much hassle.)
Remix I-17: 0:24.7 (This one isn't too bad if you can get all of the motions down. Climb up the ladders, jump across the platforms so that you can reach the platform with the ladder up to DK pretty much immediately. The bouncers may kill you. It's just a matter of getting lucky on that pattern too. The second part is a lot easier, but essentially the same thing.)
Remix I-19: 0:52.2 (I know as a FACT that the cutoff time is 52.5. This one is just vicious. Memorize the entire course, make sure you land every jump with NO bounces. If you do that, you'll get it. Otherwise, you won't.)
Remix I-21: 0:28.3 (Oh boy...this one is annoying. I believe the first two are fixed at stage left and stage right, so you can nail those two. After that, it's just making sure you hit the third one as you go up to kick. Preferably knocking it onto the center platform. Then just upend the last two and finish them off. It's easier if you do NOT enrage the last one.)
Remix I-22: 0:19.0 (This is the EXACT time required for a rainbow. (I did this one for two hours. 19.5 did not net me a rainbow. I hate this level. As far as strategies go: Pretty much always run, memorize the level, learn which areas you can skip and minimize your number of jumps. I personally would do something like "Jump, Jump/avoid or kill goomba, hit platform or land on area below, jump, jump, jump between the koopa troopa and the ? block, jump onto the high platform, run across the small gap platforms until I hit the middle one, jump onto the high platform with that, land on the stage right platform of the scale, jump onto the upper moving platform, running jump onto the upper platform, running jump onto the platform with two koopa troopas, jump over them, jump onto the moving platform, jump onto the stage right scale platform, jump to the flag." It's exactly as awful as it sounds.)
I've got a few for Super Mario Bros and Legend of Zelda too if we want to put this together...