In several months of working laboriously on this achievement (only to get cockblocked by a network timeout, or falling short by a thousand points, and on and on) I've found one strategy that consistently gets me above round 20, without fail.
As everyone attests to, the loop outside of the Comm Room is magical, and playing solo is the only guarantee of not getting flooded from two directions.
In the opening rounds, you can maximize your points however you'd like, but as long as you can grab 2500 before dogs, you're just fine. Don't worry about an accidental pistol kill, or a nuke with a handful of zombies left (often the nukes come out with <4 zombies anyway). Once you've hit your 2500, open the debris, and go grab a trench gun. The trench gun will be with you the whole time, and it will really be your best friend. Accrue another 1K, and you can get through the Comm Room gate, and then begin your loop. You can wander freely for the next six rounds, gathering perks (you'll be best off with Speed and Nog). Buy a Thompson off of the wall, as your second weapon, before round 10, and start boxing when you have free time. If the box goes somewhere stupid (anywhere but Comm, really) don't sweat it; between the Thompson and the STG, your ability to go far is limited only by your agility and quick-thinking.
Ideal weapons from the box are submachine guns. These guns, with the best being the PPSh, do their damage in round-count, not in stopping power, so the points earned from every kill are as high as possible.
Doing the loop, fire as little as you can in the body of the round, only pop off trench gun rounds when you feel your path is going to be dangerously blocked by a zombie (and of course, you better get a headshot). At the end of the round, when you see no more zombies trickling out of the center building, turn around wherever you feel you can safely walk backward, take head-level aim, and fire as many controlled bursts as you can. Your points will start to skyrocket, after round 15 you should be able to earn 7-8k per cycle, and increase from there.
One thing that gets a lot of people is dogs, but a lot of people also seem to keep an all-automatic arsenal. The great thing about the trench gun is that, if you have good aim, you'll never need to get bitten by a dog. Get your trench gun out, go crouched, and slowly pace around your preferred hiding spot, always backing away from the dogs (when a dog lunges, it calculates only for the area you are in at the beginning of the lunge, and if you move far enough out of its bite radius, you'll take no damage, and have a still-standing dog to blast).
Keep your guard up in the loop, and pay careful attention to aim, and you'll get your achievement in the mid-twenties. Higher if your aim is shaky, or if you get a lot of nukes on accident.
Resist temptation to have a friend help you, or to play with matchmaking. It may seem nice to have a safety net, someone who can revive you when you make those terrible, easily-avoided mistakes, but they will be your worst enemy when they go down on round 22, after stockpiling an apocalypse of zombies, and you have to cut through those, while being pushed by your own crowd between two fences.