While you are unable to shoot, you are still able to use your melee attack to fend off the hordes of zombies. Happily, 6 minutes isn't long enough for any of the more seriously dangerous zombies to appear. Also, there is a handy spot in the top right of the map that can be considered a "safe spot". If you wedge yourself into the small corner at this edge of the arena the zombies will have a hard time funneling their way up to you to do damage. Pair this trophy with Melee Master by standing in the safe spot for six minutes and the two trophies will become very easy. Do note though that using this method is not a good way to play long-term so you will want to restart the game after going for these trophies.
To see the safe spot in action, check out the video below: