There are 4 bonuses per level, you need a total of 10.
The bonuses are:
Low-Level Bonus - Being at, or below, the suggested level, which can be seen under the stage name.
Genocide Bonus - Kill everything on the stage, in some stages, this requires you to backtrack or enter side rooms. DOES NOT include those yellow puffer fish like creatures.
No Damage Bonus - Take 0 points of damage. DOES include hits by those yellow puffer fish like creatures.
Trinity Bonus - Earn ALL bonuses at once.