This Achievement can be a royal pain in the backside.
You must make it from the start of the level to the end of the bridge descend without killing anyone. And by anyone I mean Army and Zombies, you really get very little help from the guy you're with (despite him having a gun!)
The best way to attack this level is by running between Checkpoints, you can use your gun to shoot open doors but that's about it. Occasionally you will come across food which can really help and you also get food from Checkpoints.
You can die as many times as you like because it does not factor into the Achievement.
When you reach the end of the level and come to the Rocket Launcher guys try to sit back and allow the other guy to pick off the ones at the start but then again don't rely on him to help as you make your way up to the top. It's all about luck throughout.
I have posted an edited video of how to get the Achievement, all deaths have been taken out because there were a few.