Warp from world 1-3 to world 4
At the end of the outside section of 1-3, drop a 
potion next to the pot and  go into subspace.  Go down the pipe to warp.

Warp from world 3-1 to world 5
When you reach the waterfall go down it and land on
the platform at the bottom. Go through the door, head
right, pick up the potion from under one of the plants,
drop it by the pipe.  GO down the pipe to warp.

Warp from world 4-2 to world 6
At the whales,  run to the right, pick up the 
potion, and continue until you reach the pipe.
Enter supspace and go down the pipe to warp.

Warp from world 5-3 to world 7
You need Luigi. 
Climb the ladder into the level. Leap to 
the top platform and use the potion to go in subspace, and down
the pipe.