Easiest on the first level. Just play with a friend(s) or find a hosted game, when the level starts simply stay alive and do not fire a single round, just let your buddies kill everything.
You can also plug in a second controller locally and use it to beat the level while your main profile idles, you can even connect the ship to the second controller to make it even easier.
It is also possible to get this on levels 2 and 4 if you are by yourself, but still easiest to do with a group and yes you are allowed to die.
You will get the achievement at the end of the level.