Try doing it on your horse. Believe it or not, the knife works pretty well on horseback; just keep the aiming trigger held down and slash away. If this doesn't work then go on foot but DO NOT use bait, you do not want 3 cougars coming out of nowhere, keep medicine handy so when he lands the first hit you can heal right after getting up. Watch out after the first slash, he might try to run away, in which case chase him on horse and try to knife him. Save after each kill or you might get 1 kill, then get killed and lose the progress.
To long to read - Be persistent and save after each kill. Don't use bait.