Wiki - Journey to the Underworld
Intended for Mid-Tier or less characters, Philoctetes will refuse to give this quest to anyone with more than a 400 Stat Cap and the dungeon can not be entered if these qualifications are not met.
Part 1 - Underworld Minions
Philoctetes can be found outside the Arena in Luna. The first part of the quest is simple. Travel to the gate beneath Vesper Cemetery in Felucca, enter the Underworld, and destroy a number of it's denizens.
Defeat all the enemies that Philoctetes asked you to and return to him to get the second part of the quest.
Part 2 - Underworld Masters
Go past the Cerberus, across the river of souls, and defeat the Underworld's Masters. Phobos, Thanatos, and Hypnos. On each you'll find an object. Philoctetes requires both the slaying and the gathering of these objects to prove the adventurer is a hero. Return to him for your random reward. Rewards are on display in the display area on the world omniporter.