The club is named after Achilles (Ἀχιλλεύς) a legendary figure of the Greek mythology.

In terms of trophies Achilleas has won the Cyprus Basketball League five times, making it the 3rd most successful team on the island to date behind EKA AEL and APOEL.

[1] Several of Achilleas' players have been selected for the men's Cyprus national basketball team.

[2] Home games are played at the indoor Pallouriotisa Arena which only has a capacity for about 1,000 fans.

The proximity of fans to the playing field has given it a reputation as an intimidating and tough home ground for away teams.