Here is the full list of all 5 Late Night Drive achievements.
Complete a distance exceeding 10 km in Free mode.
Complete a distance exceeding 20 km in Free mode with traffic density set to 6 or more.
Reach a distance exceeding 8 km within 60 seconds in Time mode.
Travel at a speed exceeding 120 km/h for 30 seconds in Time mode.
Complete a 60 km distance in Free mode without any collisions.