Achilles was a character in Greek mythology. He participated in the war which destroyed Troy according to Homer. He was nearly invulnerable except for one small part of his body, which finally costed him his life. Such a minor vulnerability on an otherwise invincible enemy became known as an Achilles' Heel.
In 2365, Doctor Katherine Pulaski described Data as "sulking like Achilles in his tent," after the android developed a fixation with his own fallibility following a Strategema defeat. (TNG: "Peak Performance")
Leonardo da Vinci was contracted to paint a portrait of a local Cardinal's nephew under the conditions that the individual be depicted in the heroic mode of an Hercules or an Achilles. The end result was described as having made the "young fool of a nephew look far more heroic than nature ever intended." Da Vinci described the feat as "an act on my part far greater than anything accomplished by Hercules or Achilles!" (VOY: "Scorpion")
Henry Janeway once pointed out to his son Jason Janeway that none of the classic heroes had come from nuclear families – in fact, Hercules, Achilles and Odysseus were all products of single parent upbringings. (VOY: "11:59")