What i did to earn this is very simple but there are other ways than what i did with a lot of other combinations of cars and tracks to earn this achievement.
But what i did was play on coast and the marina, use alexa and the diamond back.
Once the race starts and you reach the first corner then hold both, the gas and brake around all corners and straights. Make sure not to crash or use boost as this will likely end your drift.
Achievement popped straight away for me.