Below is a walkthrough for the We Long for Mishy support request in The Legend of Heroes: Trails from Zero. In order to obtain this quest in Chapter 1, speak with Lars in the Long Lao Tavern & Inn on East Street after returning to Crossbell from completing the investigation at the hospital.
Once you’ve accepted the quest, head to the Entertainment District and enter Barca Casino. Inside speak with Cherry (girl wearing bunny ears at the Exchange counter). The Mishy Plush Toy can be traded for 200 medals. You can either purchase these medals for 1,000 mira or win them!
After you’ve traded for the Mishy Plush Toy, return to Lars in the inn on East Street to hand it over. As a reward, you’ll receive 120 mira and the quest will complete. Make sure to report it at the terminal!