Stars can be used to purchase alternative wands or unlock 2D puzzle levels. If you're only interested in achievements, buy puzzle levels.

To open the shop:

1. Click the home icon in the main menu.
   
   
   
   
2. Using the arrows or keyboard/pad navigate the the puzzle section.
   
   
   
   
3. Puzzle section is indicated by a large puzzle on the MC's desk. Doubleclik on a puzzle to purchase access with stars.
   

If you don't have that achievement, you are probably missing a 2D puzzle from the Home section, mentioned above. If not, there's a way to check which puzzles have been finished.

When a puzzle is completed, a star appears at the end. This example shows a puzzle which has been completed on easy in contrast with a puzzle which has been completed on hard, but the principle is the same. If a puzzle has a green star at the end of its entry, it's been completed. If not, it's missing.