To reach those higher rounds you need to get the right gear, make sure to upgrade your weapons and KEEP MOVING!
As far as weapons go I prefer the CE3 Cauterizer Shotgun as my main and something explosive as my secondary (all can be bought from the 3D printer). Pick up the contact grenades (because they don't have a timer) from the sewers and get the distraction drones from the 3D printer (great for getting out of a tight spot or reviving teammates).
Make use of the traps to thin out the zombies once you have a train going. My personal favourite is the orbital strike on the burger town roof (also the ambulance distraction is a life saver).
Now that you have the gear just stay outside and run around letting the zombies gather behind you then take cheeky shots at them all in a line. Leave one or two alive (if they are crawlers even better) and use the time to upgrade your weapons and restock grenades. Then kill the ones left alive and repeat until round 25.
You don't have to survive round 25 just reach it