Any zones you can do really well that aren't posed yet would be fine. The hardest ones for me are the Music Plant zones though.
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I just HATE Music Plant. NintenDan has a video up for that too, but it's near impossible to follow. As for lowering your time, just practice. I was stuck at ~35 seconds on LF1 for a while before I finally got down to 32.
As douglas mentioned, keeping Boost Mode is essential. I'd say in LF1 there are 2 points where it's hard to keep Boost Mode:
1. About 6-8 seconds in, you reach that halfpipe and have to jump. You have to time your airdash so that you don't get TOO much height (because that wastes about half a second or more), but if you go too low, you lose boost mode and your whole run is ruined. Most of this is trial and error.
2. The other part I often lose Boost Mode is right after the underwater part. As I jump off the swing and into the ramp, my naturally bad timing lands me right on top of one of the robots. Embarassing, yeah.
The only other tip I can provide is to practice your airdashes. I still generally suck at them, but on a straightaway (like the one that follows #1 above), you should be able to get at least 3 airdashes there. You
don't have to be as fast as the video there; that's almost unnatural speed.
Advance 3 I'm not so good at. I only have one decent time, Ocean Base 1. The main tip there is to use your ground tag action (as Sonic+Tails) quite often, as the level is more vertical than horizontal. I can't remember the exact strat off the top of my head, as I haven't played it in a few months, but you should be able to get under a minute if you do it at the right places.
I'd make a vid, but I don't have an easy method to.