From the Social menu, select Co-Op Campagin and then Invite Friend and Create Session. Once your friend has joined, fast travel to a short track such as Archway Meadows Circuit and create an Exhibition race. Change the Country to Japanese Steel and change the Race Settings to 1 Lap. Pick a car and complete the lap to get the achievement. You do not have to win.
Japanese cars are Datsun, Honda, Mazda, Mitsubishi, Nissan, Subaru, Toyota.
The 723 Quartz Regalia gift car is also classed as Japanese, but I cannot confirm if it will get you the achievement.
Races completed in Private Online Adventure and Private Online Freeroam do not count.