There are 4 tracks to choose from in the Shibuya track pack:
Head into the Singleplayer menu
Set the Discipline to Rallycross
Location - Shibuya
Track - either Yamanote Line or Hachiko Square (As they're the shortest)
And the vehicle class doesnt matter but the Rallycross cars are faster.
The 2 suggested tracks take less than 30seconds to complete, once you have completed one full lap press start and end the session.
The achievement will pop in the loading screen
Here's a video to demonstrate.