see also section on bear about bleed out times with various weapons and critical hits on the bear. Often one shot is sufficient to kill the bear if shot in the face from very close range. Once it rears up, I don't know if there is a critical hit zone but in real life, aim for the heart shot, centre of mass between the front shoulders. I have not tried this in the game (yet) due to difficulty setting it up. Two shots work if using the fire trap on the bear by shooting it in the face. Normally, a real bear is difficult to kill in this manner; the double lung shot is preferred from the side or rear quarter shot. This produces very rapid bleed out. Not confirmed in game however the arrow may actually be preferable, if you can get the right shot!