The way i got this was to start a
Hot Lap race (Via Free Play) using Bugatti Veyron 16.4 with the following difficulty settings:
Braking - ABS on (Can turn off if you wish)
Steering - Simulation
Stability Control - Off
Traction Control - OffOther settings are personal preference
The track i used was the
Sunset Peninsula Raceway - Speedway.
At the pre-race screen make sure to head to the
HUD menu and change the
Drift HUD to ON.
Once the race starts follow the track round and build up speed, once you get to the second turn hug the inside of the track and tap the ebrake (
button) and turn slightly into the corner, the car's rear will begin to tail out balance the slide till you have passed 5,000 on the drift then correct the slide to straighten the car out.
Once the score banks the achievement will pop.
Here's a video demonstration. (Skip to 1:50 for the drift)