You can play through on any difficulty level to get this achievement to pop in co-op or solo. I would recommend playing on Casual alone in order to get the most lenient speed times and intel item requirements, as well as making the enemies easier to kill. If you play with a group, the individual requirements are lower, but you seem to be graded harsher.
Several people recommend using the Riot Gun for Zombies and Crimson Heads and the Samurai Edge for SpecOps, Hunters and Lickers and long distance targets.
I also recommend using SPECTRE with his Item Detection skill maxed in order to find all the intel items on a level. This will help you know where they are when going for the Great Success achievement later.