"A corrupt judge living in Port Royal has sent one too many innocent men to the gallows. Find and kill him."
Head to the Southern portion of Kingston by swimming across, using one of the fast travel boats on the beach or a fast travel point. Once there head for the marker in the center of town. Once you enter the search area, climb one of the nearby buildings so you can see into the middle of the area. Use Eagle Vision to get a lock on your target. He will finish what he is saying then start running. Follow him on the rooftops. You can easily pull off an aerial assassination. Still, it is better to see him then hit him with a Berserk Dart to just end the matter before he can start running.