When I play in a quiet world with my son and we are each on our own ship we both are able to shoot grapple hooks when the time is right. Whoever lands the first one then has the rights to that ship. Go to quiet world to do this quest.
If you grapple it first you will see a pop up come up stating waiting for captain to board (or if the captain of ship you will see a countdown clock and button to click to board the ship). If you notice someone else has grappled the ship just move on because you are wasting you time. The only thing you can do once someone else has grappled the ship is shot cannons at the enemy on their ship and kill them off.
Navy ships are the ones with Red writing above them. A Navy flag ship (which is the type you are able to board) have a flag above them.
