Probably the hardest achievement in the game! But also easier than you'd think. It takes some mastering of the level to unlock.
During the car/driving memory, you just need to not hit any cars at all. Not just get through alive, but not hit a single car. And the problematic part is that there's very little in the way of telling you whether you've hit a car or not! Usually you'll see "glitch graphics" telling you you've hit cars, but not always. And there's not really any sound to tell you, either.
The good thing is that the incoming cars aren't completely randomized! There are patterns that you'll start recognizing quite quickly. This doesn't mean that the level will play the same every time, but rather that there will be groups of cars that are always the same. And the entire pattern of the cars in the level repeats once.
I found that there's a large chance of encountering one car followed by two trucks on the right side of the road. But they're not completely to the right, so you can pass them on the right, going all the way to the right edge of the road. I don't recall completely, but I think after that came a car and then another truck that could be passed the same way. And there are large, open areas between them. So for long stretches you can just hang to the right!
I recognized similar possibilities on the left side, but didn't use that. Other than that hanging to the right trick for those sets of cars and trucks, I just did my best to drive without crashing.
But all in all, you really need to just do this level over and over again, not giving up! It's not that long, and you'll get through it with no crashes much faster than you think! (I think I only spent about 20 minutes on this.)
Keep in mind: I don't know whether or not the game will give you the achievement if you restart the level because of death from crashing too many times! It might, but I personally didn't take the chance. So if I crashed once, I exited and continued. That places you back in the hub world, and you can just go to the right to quickly enter the level again.