Travel to the ring of torches south of the Azure Dragonshrine and blow the Emblazoned Battle Horn. Defeat Grom'thar the Thunderbringer and bring his head back to Aurastrasza at Wyrmrest.
There's no reason to suspect Dammia's words are anything but true. Whether Grom'thar defeats you or is defeated by you, she can wash her hands of this.
Follow her instructions... take the horn that you brought me earlier, travel to the ring of torches south of the Azure Dragonshrine, and blow it to announce your challenge.
When Grom'thar the Thunderbringer arrives, kill him and bring me his head.