This was funnier when I had to hunt a Giant Netch with a fork in Morrowind. The difference there is, I had a psychotic Daedric Prince telling me to do it there. Here, "Hunt the black panther with a bow," may as well be telling me to fight it with a bag of wet s***.
- Sneak down to the rocks. - Spot the kitty, with or without the use of a needle. - Land a shot with the bow. - Watch as the panther pinpoints your position and charges, pretty much ripping you limb from limb because the bow sucks.
I had a difficult time with that particular quest too, until I realized if you're far enough away, the animal just runs around aimlessly. Just stay hidden and you'll be fine. An Instinct syringe works wonders also.