Defeat Queen Merkbee, Baby Merkbees, and Chomper Merkbees near Lost Mines, then talk to Ron Harper at the Delinquent Assembly. Use your quest tracker to see your progress.
Ron Harper: Did you know the monsters here actually have a boss? NakanoAzusa: No, I didn't. Ron Harper: There is a boss in every group of monsters! Ron Harper: Without a boss, monsters are just like lost animals. NakanoAzusa: They're similar to humans, I guess. Ron Harper: Might be. How about Queen Merkbee this time? Ron Harper: She's the boss of the Lost Mines area. NakanoAzusa: She must be strong then. Sounds exciting!
Reminder Dialog
Ron Harper: Bosses are nothing indeed. The weak ones Ron Harper: around them are the real problem.