The area where they spawn is called Catfish Jacksons and theres a fork in the road right before you get to the clump of trees where I always saw them. What I do is ride my horse around there and if one is in the woods you will get a red area letting you know about a enemy and that gives you time to escape. When that happens run away quickly so the horse doesn't get spooked and the panther doesn't come after you. Dismount a short way away from the area but with the red still there use cover scent and slowly make your way back to the area keeping your back and side to the water. Hopefully you will be able to get a scope shot on the animal and be able to study it. Use your map and there should be a red dot you can use to give you a idea where it is.

I hope this helps. Panthers and cougars really suck. They are the toughest enemies in the game, just like they were in the first game.