This is something that used to bug me before I figured out what to do. In order to climb the waterfall on the Black & White level, you must jump from island to island, avoiding the giant bell shaped figures trying to squash you. When you see a fruit-looking thing, hurry over and get it. It gives you the ability to climb the waterfall.
Get next to the waterfall and push your snake against it and begin rapidly pushing the A button and your snake will start climbing it.
As soon as the game begins on level 1, run to the right as fast as you can, jump to avoid enemies, you have to be really fast. At the end of the board there is a rocket, if you jump on it in time it takes you to level 8.
When you start the game on Level 1, near the beginning of the level, there will be a small little island with no lid on it. Get onto the island and tap the B button a couple times and you'll automatically warp to Level 3.