Here is the full list of all 12 Crazy Taxi achievements. It takes around 6-8 hours to unlock all of the achievements on Windows.
You have got C class license in Original mode.
You have got A class license in Original mode.
You have got S class license in Original mode.
You have got B class license in Original mode.
You have got A class license in Arcade mode.
You have got S class license in Arcade mode.
You have got C class license in Arcade mode.
You have got B class license in Arcade mode.
You have cleared 3-1 through 3-S of Crazy Box.
You have cleared Special 1 through Special Stage of Crazy Box.
You have cleared 2-1 through 2-S of Crazy Box.
You have cleared 1-1 through 1-S of Crazy Box.