Stage select
After the coconut hits Higgins on the head, and the Title screen appears, press Right, Left, Right, Left, A, B, A and B. This will bring up the World Select screen. Press Up/Down to select an island, and press A to begin.
Continue
You must possess the Hudson Bee from World 1, then 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 the secret room.
Extra items
Enter 0894 as a password for 99 of each item.