BAJA Edge of Control

I have found that the main cause of punctures is when you hit the ground hard from a jump. To avoid this, pull on the left trigger in mid-jump, and you'll come down quickly, from a lower height. Alternatively, try to line up all four wheels before you land, making sure they touch the ground at the same time.

It goes without saying that you must try not to hit any boulders whilst going for this one, and staying out of bushes helps!

Really though, this achievement should not cause you many problems at all, and you'll probably get it without even trying.