This one is easy just have one gun with one bullet in it when you get to the final shootout when you are on the vehicle with Merle mowing down zombies you can go to your pause menu and drop all other guns and ammo you had previously to this while just saving that one gun with one bullet in it.
I should clarify basically you can have all your weapons when you are on the chain gun or whatever its called on top of the vehicle.
But like I was saying previously you want to drop all of that when you don't need them anymore, you can have everything except other guns and you will get this achievement. Just make sure when you are on top of this vehicle you don't drop that one gun and one bullet.
I actually kept a rifle with one bullet in it that I wasn't planning on using on the level anyways just so I could get the achievement. And I just dropped all my other guns from the pause menu right after I saved the helicopter on the helipad and went on to the vehicle. Its pretty easy once you know that you can pause it on the vehicle.