This achievement is won by participating in any game with both the Dominus and Takumi. This can me done in Social playlist, ranked, Season, or Exhibition.
To make this achievement easier, load up an Exhibition game with these settings:
Arena/Map: Any
Team Size: 1v1
Bot Difficulty: No Bots
Mutator Settings: Max Goal = 1
Now you can pick any team you want (it will only be you) and simply make a goal which will end the match immediately and count towards a win. Once you earn a win with one car, back out to the menu and switch to the other vehicle. Repeat process.
Here's a visual reference as to how easy and fast it is to create and finish an Exhibition map for this achievement: