Costume Kingdom

This quest will become available after you've completed the first Apex (see The journey begin's). You pick up from Luke, who is bawling his eyes out in front of a house on the left side of town:

He'll ask you to take care of Bobby, who is located on the Northern side of town (in the area with all the tires and fire in the middle). You'll need to defeat Bobby in battle to complete the Quest. Once you have, return to Luke. Talk with him to turn the Quest in and the trophy will unlock.