Defeat Chomper Merkbees and Queen Merkbee near the Entrance to Lost Mines. Then speak to Jimmy Joe Birmingham. Use your quest tracker to see your progress.
Jimmy Joe Birmingham: Not bad, not bad... NakanoAzusa: You should see what other people have asked me to kill! Jimmy Joe Birmingham: Yee-haw! I like your style! But you're still just a litte Jimmy Joe Birmingham: bitty fish in a big 'ol pond to me! NakanoAzusa: Alright, alright... Jimmy Joe Birmingham: How about you defeat Queen Merkbee along with Jimmy Joe Birmingham: Chomper Merkbees you just defeated? She'll make us Jimmy Joe Birmingham: some good money.
Reminder Dialog
Jimmy Joe Birmingham: You take my challenges in stride! Make sure you do the Jimmy Joe Birmingham: same on the battlefield!