As soon as you begin Level 1, run straight to the end of the level without stopping. If you get there in time, you'll see a rocket. Leap to it before it takes off, and you'll warp to Level 8.
In Level 1, look for the first small one-square island without a lid, and leap onto it. Press the B button and you'll uncover a hidden lid that will warp you to Level 3.
In Level 3, find the area with two pibbley dispensers. There's a lid at the very top of them. Use the speed-up to help jump across the ledges and get up to the lid. Open it to warp to Level 5.
In level 6 after the one with the waterfalls, near the begining, jump down to the sewer on level 4, here you used to recived a clock, now you will warp to level 9