You get this after defeating all the four corrupted heroes, Achilles, Atalanta, Herakles and Odysseus within their lair. So killing them out in the world map when they're hunting you doesn't count. Each has a lair in one of the main four areas, they have a different icon than the Tartaros Vaults and instead of jumping in from top like the Vaults, you have to enter them from the front, solve some light puzzles and then defeat the heroes.