Equip yourself with some OJ, a few hunting knives, and pistols. All these items can be readily found in the Paradise Plaza.
As soon as you are equipped with the aforesaid items, move to the Maintenance Tunnels. A major part of your 72 hours will be consumed here in order to get this achievement.
After you leave the Paradise Plaza, head straight into the Leisure Park and from there, move on towards North Plaza.
Just before you reach the stairs, take a left turn. At this point, you will see a fairly large hole in the park’s wall. This is the path which you need to take in order to reach the Maintenance Tunnels.
Search for a red car which should be somewhere nearby. Kill any zombies that obstruct your path. Once the car has been found, get behind the wheel and drive the car straight into the tunnels, trampling zombies under the car as you go.
At the far north end of the tunnels, you will see a large truck. Get out of the car and take control of the truck. Even though it will move at a slower pace, it will be more effective at killing zombies as compared to the car.
The truck will come to a halt after you have used up its life. From that point onward, walk on foot until you come to the far eastern end of the tunnels. This is where you will find a white car. This vehicle is fairly speedy and will help you get to your destination quickly.
Avoid driving the white car at a brisk pace because the car’s life will be reduced for each hit that it takes. Make sure you do not hit zombies carrying propane tanks because that will cause a gigantic explosion.
Drive the vehicles you come across carefully until their life expires. Search for another vehicle when that happens.
Do not forget to save your progress in the game and do save the ongoing game after every 5,000 zombie kills.
When you reach the Maintenance Tunnels, you will need some supplies. The Maintenance Supply Room is the place where you will be able to find those supplies. The room can be found right in the middle of the tunnels, at the extreme end of a passage which faces south.