This is pretty much a 'run around and look at tracks in the correct region' quest/mission.
No shooting or photographing or anything advanced at all. Just run to all the tracks you see and press X (on Xbox One, may be different on your platform)
Just be sure that you actually roam a big enough area so that you don't keep finding tracks from the same animals over again!
Hope this video helps if you got stuck on this mission!
So basically the idea in this mission is to track down a Black Bear in the Mount Kraken region of the Lake District. I started out tracking a pair of bears for 30 minutes just to have them exit the area. Luckily I managed to find tracks of another bear just near by and started tracking that one. Bears really move around in this game, and I should probably move slower in a crouched walk instead of running as much as I do.
Whenever I hear something interesting and I need to leave the current tracks, I first open the map and place a waypoint so that I can find the location later if I need to.
Remember, only the first shot needs to be in the Mount Kraken region, if you need to track a hurt animal into another region to finish it off, you still get the mission. That is pretty much what I had to do.
If you have a high level character I guess you could just buy a large predator lure and call the bear to you...