I'm writing this guide under the assumption you're starting from scratch and playing solo. Though it may not be the case, I'll give hints to how to do it with your own support. Before entering the arena with any character. You may want to acquire 2-3 weapons that are decently strong enough to handle zombies in the main campaign areas in 2 to 3 blows. The reason being that zombies in the arena tend to be weaker. Bring as many medkits as you may already have, but for the purpose of the solution, I'm assuming you have none. It'll be ok because zombies drop them anyway.
Head to Arena A with the weapons of your choice.
In the first few rounds - Rack up kills and search for some money to repair your weapons with
Rounds 5 and higher - The infected appear much more than the walkers, and a good strategy for survival is to camp on the side under the walkway that drops down which meets the middle bridge. Reason being they tend to only spawn on two sides which gives you room to run when needed. Loot thugs and Floaters for 1-2 grand each to repair your weapons and upgrade if needed.
Round 10 and higher - You'll see more suiciders appear so you won't want to attack every zombie head on. Take out a few and run so you don't get caught in a suiciders blast radius. Take them out from a distance with a gun if owned, or thrown weapon.
Round 14 to the end - By this time, the horde seems to overrun you. Just keep running in circles and dealing with small groups at a time. Suiciders run slowly along with the other big infected, so take out the fast infected and narrow your types down.
The achievement pops as soon as you hit your 15th wave with the last character you do it with. Good luck!