Successfully complete the first sixteen levels to unlock the jump pad to access the moon levels.
Play as Grandpa
To unlock Grandpa as a playable character, using Grannie, go to the level Ghost 4-4 (top right corner level in the Ghost stages). Once the level starts, climb the first set of pillars and super jump straight up. There is a "prison" there that you need the power shot to open. Once you beat the stage, you can then quit to the file select screen and press L to cycle through to Grandpa.
Play as Grannie
Collect 2,000 Diamonds and 40 Water Sprites. You can now press L at the title screen to switch to Grannie, who has all available power-ups.
Power-ups
Collect the indicated number of Golden Diamonds to unlock the corresponding power-up.
Extended Hover: 1,200 Golden Diamonds.
Power-shot: 800 Golden Diamonds.
Vertical Boost: 1,600 Golden Diamonds.