Once you have spoken with the hunter to begin the hunting challenge, your map will be updated with a large, narrow rectangular search area nearby. We need to find and kill 5 hares in this zone. This challenge is essentially the same as the previous one, just with a more generous time limit. As such, the same strategies apply!
Whilst hunting hares, I found it easy enough to simply switch on 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, hares are quite small and as such harder to hit with projectiles. As such, it is much quicker and efficient to simply use your knives on them rather than planning something more complicated.
Once you have the required pelts, the challenge will be complete.