Throughout the game after obtaining the church you'll gain some missions to complete that don't directly progress the story, they are usually centered around one of your three friends and completing them usually upgrades the weapons of those friends when they are in combat with you. They all appear in the missions app so as long as you're completing all the missions there you'll get this. I haven't marked this one as story related as I can't confirm whether you actually need to complete these missions to complete the game, but if anyone completed the game without getting this trophy let me know.

There isn't anything in game noting a mission as a loyalty mission, but I believe the following are required:

Eli