CONTAINS SPOILERS

To begin this quest, you first need to go into the menu and view the Request "Love Soupreme". Accept the quest and then you need to talk the Pharmacy Manager at the store called Akagire. He'll give you a new request that you need to accept called "The Apothecary's Connection" in which you need to provide him with materials. Once you fulfill that request you can buy Meal Tickets to finish.