NASCAR Unleashed

I suggest doing this in the first 5+ races, as it's much easier and your opponents aren't as aggressive as they are later in the game. Simply drive a bit safer and avoid damaging your car enough to require you using pit lane. I'd suggest working towards Just That Good along with this trophy.

You can also unlock this via Time Trials, which makes it even easier. In addition, you can check your progress towards this in the Trophies section at the Main Menu.