Start a new campaign with Bull (the guy in the middle on the character screen). His main firearm is a sniper rifle, so every time you see an enemy, zoom in (click the right stick) and fire for a one-hit kill. It doesn't matter where you hit enemies, just as long as you're zoomed in.
On the second level ("The Hill") there's a machine gun nest at the top of the street; every time you snipe an enemy at the nest, a new one will run over to the gun to take his place. Stay at the bottom of the street and keep sniping guys at the machine gun nest until you run out of ammo.
When you run out of ammo, restart the level and keep zooming in and sniping guys at the machine gun nest until the achievement unlocks. Since you start the level with 30 rifle rounds, it won't take long for this achievement to unlock.