Collecting ALL 3 stars is preferable but not essential when unlocking ALL of the worlds. The worlds are as follows: world 1 (Cardboard Box) Stages 1 to 25, world 2 (Fabric Box) Stages 1 to 25, world 3 (Foil Box) Stages 1 to 25, world 4 (Gift Box Box) Stages 1 to 25.
Atlas is an action-rpg with rogue-like elements where you use your ability to control the ground to fight the enemies and move through procedurally generated worlds.