After you have cleared the first outpost, there will be a sign on the side near where you came to the outpost. The sign offers two quests: a WANTED dead quest and a Path of the Hunter quest. The Path of the Hunter quest requires you to kill 5 rabid dogs with the shotgun provided or your knife/machete. Find and kill the dogs in the specified area and the achievement is yours.
Remember to skin them so you can craft a wallet and syringe holder.