This mission is essentially a repeat of the Ile des Pins challenge (number 04) and we can use exactly the same tactic to complete it with tonnes of time to spare. Remember that Killing bears are aggressive and will attack you on sight. Pressing 6 successful button prompts will have Shay kill them. We can use this to our advantage.
Once you have accepted the challenge, head northwest and use the large hollow stump to access a treetop area. From here you should be able to observe the search area below with the bears in it.
Use the treetop path here to get above one of the bears and hit it with an air assassination. Quickly skin it and then run up to the second and get all up in its grill to have it attack you. Complete the button presses to kill it.
Once you have the required pelts, the challenge will be complete.