Need for Speed Payback

The first chance you'll have at this achievement is in Chapter 3, when you do a drag racing questline. You'll see a meter at the top of your screen that has a yellow zone, a green zone, and a red zone.

As you race, you'll see a line move up the bar. When it 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.

I also found that on the first Drag, you shift three times at the start, and then when nearing the end is the 4th shift (a smaller window to hit) but if you just keep releasing RT every few seconds you never hit the next shift up to need to get perfect in. Can still easily win the race as you’re so far ahead when in 4th Gear.

This should work on any of the races really, and any that aren't straight all the way it indeed pays to do this.
But the first set of rounds is the easiest due to length and track.

I recommend the event 'Billionaires Drag' which is one of the first events - South East Map, 1 o'clock in the city area.

Used a stock Infinite Q60s which i got from buying deluxe edition.. but anything 100-200HP should work.
Later cars rev extremely high and its much harder to hit perfect shifts... especially the first shift

Hope this helps