All Stages

To do the superjump:

Get hit by the Kremling while Diddy is still next to the wall. This will cause him to jump to the top of the screen.
Grab the barrel and retrieve Diddy. You may pick it up before you actually see Diddy jump up all the way. This is fine.
Ride the rope to the next platform and run Donkey into the next Kremling. As soon as he gets hit, hold down B+Y.
Fall straight down and then immediately walk off the platform onto the next Kremling. This will start the superjump.
You will pass by a swarm of bees, the halfway barrel, a rope, a DK barrel and then a Kremling. When this Kremling reaches the left edge of the screen, let go of B. Do not let go of Y or right at all.

101%

Notes:

The cue to release B for this superjump is when the DK barrel before the Kremling reaches the left edge of the screen.
You will need to fall into the bonus barrel, which is under the screen just near the sixth bird. If you can't see it the lip of the barrel on your TV, make sure you start counting the birds.
To reach the barrel above the screen at the end, you will need to bounce on the Kremling when he is at the highest point of his jump. If you don't reach it, double back and grab the barrel out of the ground next to the first Kremling and use it to break the wall. If you lose the barrel, there is no other way to reach the bonus game, so be very careful with it.

Optimal 101%

(Lukinha)