Warp to Level 3
When you begin the game, quickly headbutt the psyko pig on the left, then the one on the right, proceed to where the Walker appears, you should see a platform and a pulsating warp. Jump up there quickly!!!
Warp to Level 5
In Level 3 (The turbo tunnel) in the last section of the speed bike obstacle course (where the walls pass REALLY fast) slam headfirst into the 10th wall. That should be a warp. (The correct wall is on the bottom of the island BTW)
Warp to Level 6
In Level 4 (Ice Caverns) when you find the platform that falls when you stand on it, go down near the bottom, then jump repeatedly so it goes back up. There should be a warp formed at the top.
Warp to Level 8
In Level 6 (Karnaths Lair) in the 2nd Snake pit, climb on the first snake and jump all the way to the right when the snake reaches the height of it's path (don't hit the spikes) there should be a warp on the other side. You must jump over because the warp will disappear before the snake gets there.
Shortcut to Level 11
In Level 10 (Rat Race), when you kick the bomb in any of the three "races", the Spazz you've been racing will generally fall down from the top of the screen and hit its head on the girder, sending you to the next segment. You still can hit Spazz in this short while with regular or double-tap charge attacks as usual; if you're able to hit the rat with a Final Smash move before you fall to the next segment, the level-finish music will play and you'll be warped to Level 11! It is debated if this is an official warp point or not.