This one's kinda difficult, not gonna lie... But believe it or not, it's MUCH easier with the AI. The AI almost never friendly fire. I'm not gonna say it's impossible for them to friendly fire, but I've never seen it happen. Make sure that you don't friendly fire either. The best way is to use a pistol the whole time. Works well with:
Double pistols works too. The fire isn't very scattered and makes things much easier. The hunting rifle also works (the achievement picture even tries to give a hint, but I go with pistols since there's an achievement for it.)
If you ever see a circle with a slash through it saying "do not shoot other teammates" (or something along those lines), then you've friendly fired and have to restart the whole campaign in order to try for this achievement again. Just resist the urge to pick anything up (I do not know if it voids the Akimbo Assassin achievement to carry another gun, so I just wouldn't).
This one is a little more advanced though, just remember:
-Go on easy on single player
-Run through with only pistols
-Be very careful when shooting.
-Only shoot when absolutely necessary.
-Melee when in close corners or boomed on to prevent accidental shooting.
The achievement description can be misleading because on Easy, it's impossible to take damage from friendly fire, but ANY friendly fire voids this one, whether you take damage or not.