I've just started running this game and noticed two things that might help out.
The simple one is in 2-5 (the level with the horses), there's a secret bomb. I believe I do the level a couple second faster and thats without great execution. There's also a full health but I don't think that really helps cos you already have full health coming in.
https://clips.twitch.tv/YummyPlausibleKumquatAMPTropPunch
The other, I don't have a clip for, but might be a big deal. In 3-6 (the level with the spitting flowers and the moving chomping plants), towards the end you use two clouds to skip some platforms on the left and just go right up the wall. At one point I messed it up, but tried to make the jump anyway... and I clipped into the wall one tile down. I was able to continue walking to the right and still finish the level. Not only would this save the short amount of time it takes to get the second cloud in that level, but if its something that's possible in other places, then it could open up a bunch of possibilities. I'll try to recreate it, but I've never used Sega Emulator/TAS tools and without save states, it might be a pain to recreate.