You must possess the Hudson Bee from World 1. Hold Left and press Start when your game is over. You can locate the Hudson Bee inside a secret room in the first cave of the first island. Jump up and down after passing the fifth skull to find the entrance to a secret room.
On the Title screen, press Right, Left, Right, Left, A, B, A, B. This will bring up the "World Select" screen. Choose your island by pressing Up/Down, and begin by pressing A.