There are two ways to complete this achievement. I prefer the first way as it simply involves playing the game.
Play the game!
The time is accumulative! You can simply play the game and drift at every opportunity and you will soon have the 3 minutes total drift time required.
Do a Doughnut for 3 minutes
You can perform a continuous Doughnut in the Batmobile. Hold drift (depends on how you are playing) and hold a direction. Collect your trophy 3 minutes later. Some people report that this will sometimes not register but if you drive at a high speed before starting the Doughnut then it will be fine!
Thanks for reading!