This quest begins immediately after 'Learning the Ropes'. Barbaras has recommended a new crew member who by his estimation is the best archer in the local region. Your task is to find him and convince him to join the crew. You should begin by sailing to a small island to the west, in Phokis.
Use Ikaros to scout the island and identify the precise location of your target. You will note the name of the archer - Phemios - and you can now approach him. When you are close enough, a tutorial tip will demonstrate how to use knock out attacks, which are necessary to bring the target to low health without killing them. When they are knocked out, you can attempt to recruit them.
You can now return to Barbaras to complete the quest, though you may want to kill the nearby bandits for loot and XP first.