chapter 5 cougar, stuck

Help, I can't get past the cougar!!! What to do? any tips? I keep dying. I keep shooting it with the rifle but no matter what, it never dies or gets injured. It's impossible to get past. I've hit it several times I think. At least it attacked, got shot at and ran away. Then it turns around and attacks again. I keep saving after each time it runs away. But, now it just attacks and I die over and over again.