Finish all the Predator's Path Quests
After you capture a Garrison, either a Predator Path Quest or a Hostage Situation (or sometimes even both) will become available to start in that Garrison. For this particular trophy, you need to finish all of the Predator Path Quests. These involve killing a rare version of an animal with a particular weapon.

To complete these quests, all you have to do is go to the marked area on the map to collect the required weapon, which will be next to a highlighted area on the map where the animal is roaming. Find and kill the rare animal in that marked zone with the given weapon. As soon as you kill the rare animal, the quest will be complete.