Here is the full list of all 12 Crazy Taxi achievements worth 200 gamerscore. It takes around 5-6 hours to unlock all of the achievements on Xbox 360.
You have got C class license in Original mode.
You have got B 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 C class license in Arcade mode.
You have got B class license in Arcade mode.
You have got A class license in Arcade mode.
You have got S class license in Arcade mode.
Clear 1-1 through 1-S of Crazy Box.
Clear 2-1 through 2-S of Crazy Box.
Clear 3-1 through 3-S of Crazy Box.
Clear Special 1 through Special Stage of Crazy Box.