I'd recommend using your left hand for this challenge for easier access to the much-used analogue stick, as well as doing the Spin Dash Jump (spin dashing and jumping immediately after) to get to farther platforms, and the Homing Attack's dash to get a slight bit of momentum for short jumps.
It goes without saying that this makes the game considerably harder, especially the more platform-oriented levels like Red Mountain, Lost World and *shudder* Sky Deck. Do the best you can and compete for the best times.
And that's about it. Have fun!
