Once you have spoken with the hunter to begin the hunting challenge, your map will be updated with a small search zone to the north. We need to find and kill 5 beavers. Fortunately beavers are easy to spot and very slow in animal terms. Activate your Eagle vision to locate them and then quickly sprint over and kill them with the hidden blade.
Although you can use air assassinations and sleep darts as described above, beavers are quite small and as such harder to hit with projectiles. As such, it is much quicker and efficient to simply shank them rather than planning something more complicated.
Once you have the required pelts, the challenge will be complete.