Eventually you will come across RARE animal hunting quests on the bulletin board at certain outposts. If you see a hunt for a golden tiger, white belly tapir, one-horned buffalo or the blood komodo, you are in luck! (There are a few other rare hunts, one involving a shark as well as a bear).
Simply accept the job, equip yourself with the required weapon and go bag yourself a "trophy" animal! The trophy will unlock upon completing the job.