In Lost Judgment, you’ll receive the Big Shame Hunter side case during The Bar with a Bite school story after you get Miu’s friendship level halfway. When you leave the bar and return, a cutscene will occur with Miu. This cutscene will unlock the continuation of the friendship meter. Reenter the bar and speak with Miu. Continue drinking with her until her friendship reaches the point where it locks again.
When you reenter the bar to max out Miu’s friendship, she’ll tell you more about the stalking. Press R3 and use the Detector on Miu’s bag then her shoes. At the park, chase after the person. When you catch them, a cutscene will trigger and the case will conclude.