You can unlock power-ups in Grannie's Attic by collecting golden diamonds:
Unlockable: --- How to Unlock:
Power-Ups: Extended Hover --- Get 1200 Golden Diamonds
Power-Ups: Power-shot --- Get 800 Golden Diamonds
Power-Ups: Vertical Boost --- Get 1600 Golden Diamonds
You can unlock Grannie if you have 2000 Diamonds & fourty Water Sprites. You will find Grannie then at your title screen.
Unlock Moon Levels
For this you have to complete all 16 standard levels.