After getting dragged to the Elven Kingdom, talk to Stan to unlock this quest. Head to Stan's house and set him as your buddy. Enter the room beside his to find Shelly.
She has a lot of HP and some damaging attacks but as long as you can inflict multiple status ailments like Burning, Bleeding and Grossed Out, you can quickly defeat her. Her attacks pack a punch so block all of her attacks if possible. After defeating her, the quest will be complete and Stan will become your friend.