Go to the rocks where you picked up the bow, and stay on them. Then lure the panther down to the ground in front of the stones by throwing stones. You have to hit it a couple of times but it dont matter cos he cant reach you.
I sat on a rock where he couldnt get me.. look the hunter damage syringe and put 2 or 3 arrows in him for the kill --- "The purpose of life, is a life with a purpose. So I'd rather die for a cause, than live a life that is worthless!!" Immortal Technique
If you shoot at him far away enough, he usually runs away instead of going after you. Wait until he calms down and shoot him again. If he runs away again, then just repeat. If he comes after you, then 1 or 2 arrows in the face will take him down. Don't forget to tag him first or use a hunters instict syringe.