This is a time-limited game. The faster you work, the further you will get. When the coffin appears, everyone should rush to it together. One player opens it while the others provide cover. Kill the hordes as quickly as possible. When a teammate goes down, revive him as soon as you safely can, because you need him/her to be killing zombies instead of laying on the ground. If your goal is to progress as many levels as possible, you have to work as quickly as possible.
Use your dynamite and other thrown weapons. They are very powerful. Dynamite, in particular, is in long supply; there's no reason to save it for a special occasion.
All that being said, the secret to winning this achievement has only two words: casual aim. Go to Options, Config and change your multiplayer targeting mode to casual. This setting causes you to automatically lock on to targets' heads, which is exactly what you need when fighting the undead. You can always change it back to normal or expert after winning the achievement. Get your teammates to do the same, and you should have no problem making it past level 14 and well beyond.
EDIT incorporating some of the comments:
1) You can expect it to take about 10-15 minutes to complete level 14.
2) The Long Shot class works really well.