This is a story related achievement.
During Chapter 3, you'll unlock a drag racing questline. This will be the first time the game has you drag race. These events involve manual shifting, where you hit a button at the right time to shift into a higher gear. The races themselves are best out out of three and best out of five. Finish all the events to unlock the achievement.
During the race, you'll see a meter at the top of your screen that has a yellow zone, a green zone, and a red zone. At the start of the race, you want to rev your engine so the line is in the green zone. You can either time it right, or rev your engine to hover within the zone. During the race, when the line reaches the green zone, press
to shift up. It will then say 'Perfect shift' if you hit the mark. Do this each time you shift during the race, and at the end of any round you'll unlock the achievement. The rounds are rather short, and the hardest part is when you're starting the race and the line is moving quickly through first and second gear. Most of the tracks are straightaways, so you can focus more on the bar up top instead of avidly staring at the streets.
Note that side bets are deducted no matter what. So if you do restart the race or lose, you lose the initial investment. So if you do have trouble on a race and have to restart a few times, keep in mind you lose your side bet money each time.