You will receive this quest during your first meeting with Hades, which will take place right after you kill Cerberos in the Guardian of the Gates quest.
To quell the chaos of the underworld, Hades demanded new Guardians for his gates. They were no Cerberos, but their combined might would do the job.
Herakles the Legendary
Underworld
Achilles the Trojan War Hero
Underworld
Perseus the Gorgon Slayer
Underworld
King Agamemnon of Mycenae
Underworld
Hints:
You must find them, defeat them in the battle, and thus convince them to become guards. In most cases they are located in places to which access is restricted by Tartaros Veil, so in order to get to them you have to complete the Beyond the Veil quest and thus get the Armor of the Fallen.
Map location: Perseus the Gorgon Slayer
He drops Cursed Gorgoneion (Legendary Sword), and Perseus's Note (Quest Item).
Map location: Achilles the Trojan War Hero
He is inside the Hall of Maniai so you need the Armor of the Fallen to get to him. He drops Cursed Spear of Achilles (Legendary Spear).
Map location: King Agamemnon of Mycenae
You will find him in the Pit of Deprivation, in its part protected by a Tartaros Veil so you need the Armor of the Fallen to get to him. He drops Cursed Bow of Hades (Legendary Bow), and Agamemnon's Note (Quest Item).
Map location: Herakles the Legendary
He's behind the Tartaros Veil so you need the Armor of the Fallen to get to him. He drops Cursed Mace of Herakles (Legendary Heavy Blunt).
Reward: Legendary XP