As I stated earlier, you should go below deck and meet Niko. It is quite obvious which way you go below deck - through the door.
After heading through the door, head down the nearby staircase. You shall meet Niko, another pirate flunkie. He challenges you to go across a set of platforms that rise up only when a switch is pressed - and only for a short time at that! (Precisely, it is about sixty seconds.)
The main worry is the timing of letting go - let go (press A on the rope) about halfway through the swing TOWARDS the destination. Remember, if the angle is bad, press and hold R to stop swinging, then use the Control Stick to rotate. If you fall, return to the ledge and press the switch that is protruding out of the ground, then the one that starts the course.
Outside, Tetra calls from the lookout platform; climb up the nearby ladder to get to her. She shows you the Forsaken Fortress and gives a brief history of it. She also mentions that there is a window with seagulls nearby - probably where Aryll is being held captive. One problem - the ship cannot get any closer due to the searchlights. The solution is the only one available…
You see Link loaded and tied into a barrel that is on a catapult. As you can tell, Link has found out the plan, as have you. The pirates plan to shoot you through the window! Tetra tries to soothe Link by claiming that they do this all the time (I never heard of this, myself).
Link is then shot off at a high speed - and slams HARD into the wall (what did I tell you?). The sword also falls down, and Link falls down even farther (amazingly, unparalyzed!).