This is a fairly easy achievement. Just like the description says, to get this achievement, complete 6 Hunting Quests. This can be completed pretty early in the game.
I would say its best/easiest to go for this achievement after having completed the "Deliver Us From Evil" achievement (Liberate 12 Outposts (Campaign only)) as there will be more outposts available to fast travel between and choose from. However, this is not required.
Basically, look for an icon on the mini map of a man running, a man with a rifle, or a chunk of meat (bait). Go to the location on the map to start one of the quests.
In Supplies quests, you will be tasked with hunting a certain kind of animal with a certain kind of weapon and returning the animal meat you get upon skinning the animal to a certain location. (Example: Hunt 3 Boar with Arrows and Bolts)
In Control quests, you will be tasked with eliminating all of a certain kind of predatory animal within highlighted areas. (Example: Kill all Honey Badgers at a given location)
In Survival quests, you will receive word that a group of people is under attack from a certain kind of predatory animal. You will be given a location and told to protect the people in that area. You and one other person must survive the encounter in order to complete the quest. (Example: Survive the Bengal Tiger attack)
The achievement will unlock upon completing your 6th hunting quest.
It should also be noted that you can check the number of Hunting quests completed by looking under the "Progress" tab in the menu.