Alexander the Great claimed descent from Achilles through his mother, Olympias. Olympias belonged to the royal house of Epirus, whose rulers traced their ancestry to Neoptolemus, the son of Achilles and the Trojan princess Andromache.
This lineage was part of Greek heroic tradition rather than a genealogy that can be independently verified in the modern historical sense. It nevertheless mattered greatly to Alexander’s identity. Achilles was the central hero of Homer’s Iliad, and Alexander reportedly kept a copy of the epic with him and admired Achilles as a model of courage, fame, and youthful glory.
Alexander also connected himself to Heracles through his father’s Argead line. These two heroic associations linked him to both Greek myth and Macedonian royal tradition. His visit to Troy, where he honored Achilles at the hero’s supposed tomb, reinforced the comparison.
A common mix-up is confusing this maternal descent with Alexander’s claimed descent from Heracles, which came through his paternal dynasty. Perseus was another important mythic ancestor associated with Macedonian kings, but he is not the answer to this question.