Speak to Abas at the entrance of Sunfall to start this Errand. He’ll tell you to go find a healer called Ghaliv nearby, so first things first is to go speak to him in Blazon Arch. When you do he’ll tell you that he’ll heal the girl if you bring him the heart of the Thunderjaw that patrols nearby. Not asking for much then. Head to the area where the Thunderjaw is at the Valley of Omens and get ready for a battle.
As usual with Thunderjaws, take out its disc launchers first then use them to deal a bunch of heavy damage to the Machine. When you run out of ammo, either fall back on blast wires, blast sling bombs or hitting the now likely exposed heart to finish it off. When it goes down, loot it for the heart then return to Ghaliv, who is now at Sunfall. Talk to him, then Abas, to finish the quest.