Thie Achievement is for completing all 10 Class 4 Administrative Zones and despite the what the Achievement description says it is not worth bragging about. Simply just defeat the waves of enemies which are all the same type of enemy (Dragon, Undead, Fiend ect) and range from Lvl 1 to Lvl 65. You will unlock these at different parts of the story by speaking with Pirates with an Exclamation mark above their heads.
Each arena is unlocked when you are high enough to fight in it so you dont have to wait to complete the ones you unlock. Each arena also contains a Katz Chest so dont forget to bring your souls! The locations are as follows:
Aberrant Quarter
Beast Quarter
Crustacean Quarter
Winged Quarter
Apodous Quarter
Demihuman Quarter
Undead Quarter
Fiend Quarter
Armored Quarter
Elite Quarter