Mystery Girl Rescue is a Story Quest in Xenoblade Chronicles. It is received after finding a passed-out girl in the Contaminated Area of Makna Forest. When Shulk goes down to the Lakeside to find the Water Ether Crystals, a story event appears, Shulk is ambushed by a Telethia, and Alvis comes to save him and teach him another Monado art, Monado Purge.
"You found some Water Ether Crystals. These should be able to help save the girl now."