To get this, you must reach set speeds WITHOUT using Nitro.
The following video is very helpful on how to get this achievement. However, he didn’t list the info for what he used and on what course so I’ll give that to you now. The format is CLASS (SPEED REQUIRED)– CAR on EVENT# of CAREER MODE SECTION:
Class D (150 mph) – Chevrolet Camaro (Rat) on Event 2 of Proving Grounds
Class C (160 mph) - FOOSE 69 Camaro on Event 3 of Crash and Burn
Class B (175 mph)– Volkswagen Golf W12 650 on Event 1 of Ruthless Aggression
Class A (200 mph) – Dodge Challenger SRT8 (Race) on Event 1 of Double Damage
***NOTE*** - You do not need to finish the race in order for this to count! Once you see that stat tracker in the bottom left corner pop up, you can press START and select QUIT. Your progress on this achievement is saved once the stat tracker pops up.
EDIT: Changed my terminology from Race to Event to avoid confusion.
EDIT #2: xLSx willard3 reports that airbrake does work. However, since I only rented the game I cannot test this out and confirm it myself. However, follow my guide and you won't even need to try using airbrake. Regardless, thanks for reporting this info willard!
EDIT #3: We have 3 confirmations that airbrake DOES work. Thanks to all who tested and confirmed.