To unlock the jump pad that gives you access to the moon levels, you need to first complete the regular sixteen levels. Once done, Grannie will give you permission to access the moon. Note: Completing the secret levels does not count towards unlocking the moon.
After collecting all the 2000 Diamonds and 40 Water Sprites in the game, press the L button on the title Screen to switch to Grannie. After that, start the game. Grannie has all of the available power-ups in the game to use at once.