Equip any hand gun in the handgun slot - it doesn't matter what gun as long as it is not an SMG, and it is fairly easy to differentiate between them.
Now play though a few levels, especially using the handgun to kill off the enemies. Within a few levels, you will have unlocked this achievement.
A good place to grind kills is in the training mission, in the final area where you are told to co-op snipe the gas tank. Enemies in this area are numerous, and if you get up to the part where you are expected to use the turret, it can be especially easy.
Enemies can not get to where you are, and if you do get downed, your co-op or AI buddy can easily heal you, because the cover will defend him against fire.
Just make sure to put AI on passive, so you can net all the kills for yourself. It doesn't matter how many enemies you have at your expense - you get none towards the achievement if the AI buddy manages to kill all of them.