Very simple achievement.
You MUST use the same car. I used the DeLorean DMC-12 in D, C and B Class. Change the tune between races. Check that whichever car you use can take three different classes of tune before you start.
You MUST race on a circuit not on a sprint
You must play in Rivals mode and beat the Rival, it does not matter if you don't post a clean lap only that you beat the rival. Posting a clean lap against a rival that has a "dirty" lap and not winning does NOT count.
You can do the same circuit 3 times just remember to change the tune between races.
Others have reported it being buggy, I don't think it is, follow the above and it pops first time.
Enjoy