Here is the full list of all 8 Fight Angel Special Edition achievements. It takes around 1-2 hours to unlock all of the achievements on Windows.
Customize to create a new role
Clear the training levels.
Have your first fight outside of Training modes.
Clear 1 course in Story mode.
Clear 1 course in Arcade mode.
Clear 1 course in Arcade mode with your custom character.
KO opponents in a round, without any harm.
Complete a local Versus mode.