First, check out "l Absolution l"'s solution and my comment to the "It's a Trap!" achievement. Doing that should help you get at least two perks, and if you play your cards right, eventually two achievements.
Now that you've read that, continue on here.
If you haven't, shame on you. But here's a very quick rundown anyway of which way to go: Fishing Hut, Storage, Doctor's Quarters, Comm Room.
It seems like two or three players is best, as the points are divided less with fewer people, meaning more points early on. THAT can certainly help you out, but not a must.
Don't worry too much about getting a great weapon from the Random Box if your goal is to get this achievement. You want to get this achievement as early as possible, and you should be fine with the Thompson and the Trench Gun. Keep your points for the doors and the perks.
Next, you want to leave the Comm Room hut for last because you'll want to leave this area for a safer fall back position. I call this area simply "The Comm Room Spot." It's just the small entry way/hall to the Comm Room with the stairs to your right (DON'T OPEN UP THE STAIRS IN THE FIRST ROOM! LEAVE THIS BLOCKED!). Zombies don't surprise you from behind, and the Devil Dogs can come from only one direction. It's a great spot to run to and breathe or acquire more points in between hut runs.
Part of this is also luck of the draw as the Perk-a-Cola machines are random at each hut. You may have to get Sleight of Hand first, which costs the most, or Quick Revive, which costs the least. Whatever happens, when you get to a hut, stay there until you get enough points to buy the perk, that's obvious. Hopefully you will, you'll have covered the entry to the hut and whatever windows are in there, and once you get a feeling that the round is almost over, take off and either go back to the Comm Room Spot or, if you have enough, the next hut in the same round, as zombies will be few. Repeat until the Comm Room is your last destination.
Make sure you have enough ... 1000 to open the doors, 750 for the huts, then the perk itself.
Let me know if this worked or didn't for you. I did it with just one friend (Benito Arf), so you should be able to!