In order to get this achievement, you just need to beat the game. Once you kill the final guy, the game will end and the achievement will pop up.
I recommend using Ross for the final level of the game because he can take more damage then any other players. At the beginning of the final level, there is a shotgun. It is hidden behind Ross' special move. Switch the shotgun for you pistol and try to save as much ammo and as many grenades as possible for the final part of this level. Try not to die, because if you do, you will loose the shotgun.
If you do happen to die, there is another shotgun spawn right through the final door before the boss. Instead of taking a right, go left and there should be a shotgun in that room.