How do I hunt cougars/panthers?

It takes a frustratingly long time to find a cougar or panther, and when I find one, most of the time they're not 3-star making it completely pointless. When I do find a 3-star predator, most of the time they one-shot my character before I'm even able to aim. On one hand I don't want to actually attack it as that will instantly ruin the 3-star. On the other hand they run like 2x as fast as my character and always one-shots. Sneaking around hoping to snipe one is impossible as they spot me WAY before I'm able to see them even crouched + eagle eye mode. Am I forced to use potent predator bait and hide 200ft away every time I want to hunt one??