This achievement can easily be obtained by going to the Arena District in the Imperial City at the arena.
4 bosses will appear in the following order:
The Devourer (A Clanfear)
Uzzai (A Harvester)
Migoruz (An Ogrim)
Dredaza the Ringmaster
Once you kill all of them, you should get the in-game Imperial Arena Champion, as well as this achievement.
The achievement seems like it can be pretty glitchy at the moment, so if you are unsure of which boss you still need to kill, just go:
Journal ---> Achievements ---> Alliance War ---> Imperial City ---> Imperial Arena Champion