The achievement unlocks when you equip a platinum badge that you have unlocked.
The fastest and coolest way that I've found was unlock the 'In The Draft' Platinum NASCAR badge. I've used the MasTRE007's guide for the 'Dirty Air' Achievement (less the NASCAR Car, cause I dont have the DLC), and have complete the achievement in under 25 minutes.
So when you reach the mark of 100 perfect drafts, the Platinum Badge shows up. Just change for this Badge and the Achievement will pop.
NOTE: You also will complete the 'Geared Up' Achievement equipping this badge. Doesn't need have the NASCAR Expansion. 3 Achievements in One Run :)