This is a series of missions where the objective is to hunt down animals to earn the respect of the Rakyat. You must use the weapon and ammo provided or a melee weapon. Find the animals in the hunting zone. There are times that you just need to kill an X number of them but most of the time, you'll have to skin them. This is usually the case for the rare animals. Their skins are necessary to craft the top tier equipments. New Path of the Hunter quests are unveiled in the bulletin boards of liberated Outposts.
After completing a few story missions, you'll have the ability to craft the Animal Repellant. You only need two yellow leaves and this will prevent any hostile land animal from attacking you. This is practically useful against any hostile land animal.
Example of normal, low level hunts
Rare Golden Tiger
Mosquito Yard Outpost Bulletin Board
Black Panther Hunting
Blood Komodo Hunting
White Bellied Tapir
One Horn Buffalo
Camp Murder bulletin board
Yellow Neck
AM12 Bulletin Board
Undying Bear
Cradle Gas bulletin board
Maneater Shark
Kell's Boat Repairs bulletin board
It will be a challenge to kill and skin it so you may want to have some crafted syringes with you, especially the one that prevents damage (Untouchable) so you can safely dive, skin the maneater carcass and ignore the surrounding sharks for 25 seconds. The Shark itself has a distinctive color so it's hard to miss.
You can also use the patrol boat and use the mounted gun to kill the normal sharks around and use it as a hunting platform. Remember to use the camera and Hunter's Instinct to track it down.