Warp to World 4: In level 1-3 go to the area just before the brick background. Pick up the plants until you get a bottle. Then go past the brick background until you find a pot and throw the bottle on it. Go through the door and down the pot into World 4.
Warp to World 5: To warp to level 5, first get to level 3-1. When you enter the first door, fall all the way down. You have to be in the middle as you fall. When you stop, you will find a platform with a door. Enter the door, then look for the potion in the grass. Pick it up, then throw it on the ground, enter the door in cyberspace, and go into the vase and you will be at level 5.

Warp to World 6: In level 4-2 In the area with the whales find a bottle and throw it on the next pot. Enter the doorway and go down the pot into World 6.

Warp to World 7: Work your way to level 5-3. (It would be a good idea to choose Luigi for this level because of his superb jumping skills.) Go up the ladder at the beginning of the level, and then jump up onto the ledge above the ladder. As soon as you get on top of the ledge, grab the first grass on the right. It is a potion. Use the potion and go through the door. Now, while in sub-space, go down through the jar and voila! Now you're in Level 7!