Method 1
Use any character and run right toward an enemy at full speed. Just a split second before you think you're about to get hit, jump! With good timing you'll be able to jump yet again in midair!
Method 2
This is yet another way to jump in midair. Stand on the ground while you have 3 or 4 life units and let an enemy run right into you. You'll lose a life unit, but you'll be able to jump in mid-air.
Flying Logs
This is most easily performed in World 1-1. Grab a POW block, and carry it to the set of logs. Wait for a log to bog over the waterfall, then throw the POW block so that it hits solid ground. For some odd reason, this will cause the log to fly high into the air.
Warp to World 4
Go to world 1-3 and find a potion. Now find the vase next to the brick building all the way to the right side of the level. Drop the potion and go into Sub-Space and then warp into the vase (stand on top of it and press down) You will warp to World 4!
Warp to World 5
Go to world 3-1 and go through the door to the large waterfall with all the clouds. Now jump down and land on the platform in the center and enter. Take the potion and drop it near the vase. Enter Sub-space and warp through the vase (press down on the vase) You will warp to World 5!
Warp to World 6
Go to world 4-2 and get the potion. Now find the vase and put the sub-space door next to it (drop it from atop the vase) Now enter sub-space and warp. You now warped to World 6.
Warp to World 7
Go to world 5-3 and get the potion (make sure you can squat-jump to the vase, you need to get someone with a good jumping ability or use an enemy to give you a boost.) Put the sub space door near the vase and enter sub space and warp into the vase. You are now in world 7!
Double Jump - 2 Methods...