The trick to Perkaholics Anonymous is firepower- lots and lots of firepower. You are going to want as many upgraded Ray Guns as you can get your hands on, as well as an upgraded Wonder Waffle. If you are having bad luck at the box and can't get the Ray Gun, then the Trench Gun upgrades into a powerful shotgun (the "Gut Shot") that will remain a 1-shot kill well past level 20.
Once you've got some serious firepower, go into the room behind where you turn on the power (the room where you get the bowie knife). By the teleporter is a dead-end hallway with a window halfway down. Have one person (someone without a ray gun) crouch next to the window, while everyone else goes further down the hall to provide support. The guy at the window is responsible for any zombies at the window, and everyone else is responsible for making sure no zombies sneak up on the guy at the window and kill him. It would help if the guy holding the window had Juggernog, but it's not necessary- when I got my Perksaholic, it was in a 3-player game, and none of us had any perks.
Have the guys in the back unload ammo as fast as they need to to ensure that nobody touches the window guy. When you start running low on ammo, tell the other support guys to reload so that, by the time you're out of ammo, they should have a fresh clip and you can reload in peace. While it's tempting to look out the gaps to the left and shoot zombies there, if they drop any powerups you won't be able to collect them, so I wouldn't recommend it. If someone goes down, have someone toss a monkey bomb out the gaps to the left and then revive while all the zombies are distracted. For dog rounds, be quick on the trigger to kill them all at the bottom of the stairs, but don't worry about using your Ray Gun if one gets close; the upgraded Ray Gun's blast deals much less damage to you. You can still kill yourselves by firing 4-5 close range blasts in rapid succession, but a single shot of the upgraded Ray Gun will never kill you, no matter how close you stand to the blast. After that, it's just a matter of time before you hit round 20. As I said, I made it with 3 players (one Ray Gun, one Wonder Waffle/MG42 combo, one Trench Gun, all of them upgraded) without a single down. It seems like a tough achievement, but the upgraded ray gun makes it really easy.