Achilles was a popular gladiator on 892-IV in the 2260s.

In 2268, he, together with Flavius Maximus, was chosen to fight the "barbarians" Spock and McCoy on Empire TV. Achilles was assigned to fight Spock; Spock tried to reason with him, but Achilles was determined to win. When McCoy came into trouble, Achilles was easily knocked out by Spock. (TOS: "Bread and Circuses")

The role of Achilles was played by Max Kleven.
According to the script, Achilles name was "Maximus Achilles" and his lines throughout were scripted as "Maximus". The following description is also stated in the script, "The Gladiator Maximus, unusually large, burly, efficient looking."