You first unlock the ability to do challenges on level 2. It is very easy to get this trophy on level 2, the challenges are:
Two-fer: Kill 2 of The Possessed with one trigger pull from the Shotgun
The possessed enemies are the weakest enemies that you encountered at the start of the level and throughout. You should use a weapon mod on the shotgun for this. If you have the burst charge then you should charge it up and line up multiple Possessed enemies and hope to get 2. If you have the explosive shot then fire at the ground near 2 Possessed enemies.
Variety is the Spice of Death: Perform 5 different glory kills on The Possessed
To perform different glory kills you should aim for different body parts each time. Each leg, each arm, behind or in front of them will each perform a different glory kill.
Quite the Explorer: Find 3 secrets
If you have trouble finding 3 secrets then you could follow my level playthrough video. The description contains timestamps for each secrets, codex, etc: