Jake said:
...clicks the mouse button, and I accidentally thok...
Wait, why, who what-- why the MOUSE for jumping? I know it might seem a means of ease, but the mouse is sort of a bad idea. Fingers on the mouse usually let themselves rest, and you end up holding down the buttons without realizing... But anyway, I've always found wasd with space to jump and shift to spin was pretty worthwhile on its own, simplistic... etc. etc.
ANYWHO!
To add to what Mystic said, I'm pretty sure EVERY level in the game is made to be finished with tails, if Tails couldn't fly. That is to say, even with his low speed, you should be able to finish any level with only the use of spinning and jumping.
Outside the special stage tunnel, you want to keep careful, accurate jumps. You'll note that all the rings in this stage are placed super-close together -- ease of gathering on such tight platforms.
Inside the tunnel, make sure your head doesn't slam against the ceiling. Try to jump when the target, down-moving platform is at the middle point between the rings and ceiling, as to just graze the ceiling, and land on the next platform as it passes the rings. (The only problematic point here is the middlemost platform, as it's a stack of these ring formations...)
Personally, I suggest getting the rings outside the tunnel first and foremost. Going through the tunnel takes more time than going around the outside. The outside has much thinner flooring, and it's really a bad idea to suddenly feel rushed by the timer, here - you'd fall off before the last 5 rings.