The Trinity bonus is received at the end of a raid mission, only when all other bonuses are awarded at the same time.
They bonuses are as follows:
No Damage Bonus:Awarded when you complete the mission without receiving any form of damage or taking any kind of hit.
Genocide Bonus:Awarded when you defeat every enemy in the stage.
Low Level Bonus:Awarded when you complete the level at the recommended level or below.
The best way to go about this is to first set yourself at the recommended level before starting the level by pressing L3 while highlighting the Character Option. If you have trouble obtaining the other two bonuses, come back once you have better weapons or have a partner to assist you.