Choose single play and choose the track hawaii, than get a good car to drift with e.g. an bmw. Play the track until short before the end of the round, there is a long left-curve, break with the pedal and drift slowly. Maybe its good to get some speed before you try this out. It has to be 1000 m in one drift, the achievement did go up after the drift has stopped.
If you didnt do it switch in the controls to hand control set so you can drive a lot easier without moving the phone.