Once you have spoken with the hunter to begin the hunting challenge, your map will be updated with a large search area nearby. We need to head inside and track down the animals required for the objective.
This challenge is a little trickier than most of the others as you will need to hunt two different types of animals at the same time. The game will give you quite a small search area and have you hunting deer and elk.
Note that the elk can be spotted quite easily due to their size and like the wolves and bears is an aggressive animal that will attack you if you provoke it, so doing so will definitely save you some valuable time rather than trying to stalk it.
The deer on the other hand act a little strange during this challenge. As there are quite a large number of them within a fairly small search area they are constantly acting skittish and will run around everywhere. Whilst it is possible to air assassinate one or two of them, it is probably just best to use your sleep darts to take them down and save yourself some frustration.
Once you have the required pelts, the challenge will be complete.