You will earn a star when you score at least 1,500 points on each world. Each level has the following bonuses that can be added to your score.

+25 Complete: Complete the level.
+50 Perfect: Complete the level without losing a life.
+25 Hoarder: Complete a level with all items.

Each world has the following bonuses that can be added to your score.

+100 Complete: Complete all 12 levels and defeat the Boss.
+1000 Immortal: Complete the world without losing a life.
+100 Frugal: Complete the world without buying any items in shops.