Dreamless by Josephine Angelini

Tasked with descending to the underworld and killing the furies so that the Scions can stop fighting amongst themselves, Helen must endure hellish torture whenever she goes to sleep - she wanders around the various levels of hell with no idea how to complete her task, and she's beginning to suffer from extreme exhaustion.
Helen carries on with her mission, and for the first time meets another person down in the shadowy underworld: Orion, descended from Adonis and with the power to control desire, he is the heir to the house of Rome and an outcast. He's also kind of hot. Confused by her conflicting emotions but glad to have an ally in hell, Helen begins to realise the enormity of her task...