Here is the full list of all 18 Nurbits achievements.
Completed the basement song
Completed the club song
Completed the arena song
Completed the spaceship song
Achieved a three star rating on all puzzles in the club song
Achieved a three star rating on all puzzles in the arena song
Achieved a three star rating on all puzzles in the spaceship song
Achieved a three star rating on all puzzles
Achieved a three star rating on a puzzle
Scored over 200 on a puzzle
Improved your score by replaying a puzzle
Overloaded a Preplaced chip
Exploded 5 or more chips at once
Completed a puzzle you designed
Added an effect to a created loop
Used 3 effects on a single loop
Added a note to every square on the grid
Opened the credits