GesterX's solution is correct, but there some ways to make the process much easier.
Since you only need to not be hitting racers and racing cleanly in terms of the track and difficulty doesn't matter I would suggest to worrying about cleanliness at the start of race. In addition, consider turning the driver difficulty (drivatar) down to its easiest. Then focus solely on getting into first place. Once you reach first drive your safest from there on out. This will stack clean racing skills for the remainder of the race.
Using rewinds will eliminate your clean skill and will not restore your clean skill if you hit something.
Just get 100 clean, great clean, awesome clean, ultimate cleans, or clean starts to unlock the achievement.