Go to the following location in the open world (also shown in the video). You can go there at any time. There is a safehouse/respawn point there. A car is parked in front of the respawn point. There is a good chance it is a "Berkley Gypsy". If you get a different car, kill yourself and you will get a new one (or drive away and come back later). Drive the car up the road, and then drift through the mud on the left side of the road. To drift, hold the brake and handbrake for a short moment and pull the left stick all the way to the left/right. You must drift for 5 seconds or longer in one go to get the "New Bordeaux Drifter" achievement.