This achievement is not possible with Brave New World. You will need to disable it by going to the main menu -> DLC and unchecking BNW.
To get this you need to use the Ottoman's unique ability to capture barbarian ships. Sail your ship adjacent to a barbarian ship and you will have a 50% chance of capturing it. Note that if you fail the capture the ship will be uncapturable for the rest of the game so you should destroy it to remove confusion over what ships are eligible. I recommend doing the archipelago map since almost every barbarian ship will be next to water and capable of spawning ships. Station ranged units next to camps to kill all non-naval units that spawn and have a ship camped nearby to speed things up. After you capture your tenth barbarian ship the achievement will unlock.