This can be one of the shortest or longest boss battles in the game, as there are multiple ways to fight him.
METHOD 1: If you fight him directly, use the thermal goggles and when you first spot him, don't snipe! Put on your best camouflage and sneak up behind him and hold him up. Point your gun at his head 3 times to shake off his camo, which will take away his ability to auto-recharge his stamina. He will then start to run, but keep your thermal goggles on, he leaves incredibly obvious footprints. Another thing you can do to make it easier is to shoot his spotter, that little green bird he has.
METHOD 2: Set your console clock ahead by a week. When you load the game up again, he dies of old age. (Although I haven't seen this myself, others have said this does not get you the achievement)
METHOD 3: See achievement THE EARLY END