This achievement will pop after you get through the section with the word "wheels" everywhere. Highlighting wheels with your flashlight will make a car spawn. Spawning a car will not affect the achievement. Infact, I recommend it. Spawn every car and use them for cover. The achievement is for not DRIVING.
First, spawn the first car. Then run towards the monster truck. Try to pass it if you can.
Behind where it started to attack you should be a large cylindrical piece of cover. The cars can't get in the back corner behind it very well, so use that to lure them up and take them out.
At this point 2-4 Taken will be walking towards you. Shine them and blast them.
Once you have killed all the Taken and both trucks, book it towards the light in the distance. A few Taken may spawn as you run, but they should be avoidable.
Under the light is the button to open the door you need to get through. Don't press it yet. Instead, let yourself fully heal. Pressing the button shorts out the light your standing under. You may also take this opportunity to kill any stragglers that are following you.
Now, once you press the button a few objects will become possessed, and 2-3 Taken will spawn. Run to the right, into the corner, and take care of them. Then shine your light on the words "Red Box" for supplies.
Start to cut right through the field. About halfway 3 more Taken should spawn. As this happens another object becomes possessed. Deal with them right then, don't run.
Once you reach the gate, look inside. You will see 10-15 Taken staring at you. Just shine and blast. They die pretty fast, and are deep enough inside so they don't pose a threat.
Once the room is clear walk on through. Up the steps. And hop down. Once outside and on the ground you will get your achievement.
Mine popped as I opened the Red Box to the right of the back exit.
A tip from the user Hurball:
"I can add that if you accidentally get in one of the vehicles then simply reload the checkpoint, it doesn't stop the achievement unlocking."