the base quest achievement is when you see the All Zombie must die! on the screen then you must kill between 60 and 110 zombies on that map in order to make it safe for the base. You must kill all those zombies without getting hit once. I suggest that you do this at the first time the AZMD shows up at the police station. You only have 60 zombies to kill and most of them are normal zombies + some swat ones. Make sur you have at least 1-2 swap bombs too, it can help you a lot for killing multiple zombies.
If you can find a shield too, that will help too. If you get hit, just let you die, you will respawn at the same map.
100% Completed games (including DLCs)
100% Win8 games: 8
100% WP7/8 games: 31
100% retail games: 46
100% XBLA games: 49