In order to obtain the Trinity Bonus, you must get all three bonuses in ONE RUN.
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.
If you're having trouble, keep playing and earn more powerful weapons and mods for them, then retry the first level at the suggested level. You should be able to blaze through at level 10 gear easily.