Getting through the game as fast as possible means going as fast as you can. Holding down right in this game makes you go faster, so you want to hold right as often as possible. Some jumps are really difficult to pull off without at least some slow down, like the second moving block in level 2. If you slow down for a split second before the jump it'll be a lot easier to time it correctly because the block flips around and you won't e going towards it at lightning speed.

Another mechanic in this game is sometimes you can flip gravity. When you go over one of these gravity flips, you want to switch which key you're holding just before you get flipped, it's just a tiny bit faster. An exception is level 19, where you actually want to throw away a bit of time so you can fit through the spinning blades at the end. Press the key after getting flipped to get a good pattern in 19, but press it before getting flipped to optimize for speed.

Lastly are the layer jumps. By pressing R, you move from the blue layer to the orange layer and vice versa. Usually they aren't directly next to each other and you'll have to jump and press R mid-air. Try to change layers and change your direction at exactly the same time, preferably at the the peak of your jump to lower your chances of dying. You can't change layers and change back before you land, so if you change while there is no other layer, you're dead.

Also, when you start a level, make sure you don't just continue holding right from the last level. It won't give you max speed for some reason.

And that's the basics.