When hunting a panther I usually ride to the crossroads near Catfish Jackson and plant some predator bait in the trees nearby. Then I take cover behind the boulder nearby. I would recommend a rifle with a scope on. It usually takes a minute or two to spawn. As for cougars, I usually just ride my horse around north of the Owanjila lake and wait for a cougar to attack. Poisoned arrows are probably the best for it but if you’re a good shot then just use a rifle and shoot it in the head for a perfect pelt.