Early the next morning, Vyse is woken by a treasure-hungry Aika. Climb down the ladder and talk to Dyne; he'll give you your share of the spoils from yesterday's raid - a Purple Moon Stone, which allows you to change your weapons to that color and learn Purple Magic. Once you go outside, you'll meet Aika and Fina - Fina will be staying on Pirate Isle for the duration of this adventure.
Head up the wooden walkway to the smaller island where your boat is waiting, and you'll also find a couple of people to talk to. When you're done, walk up to the boat and press 
to board it.
Traveling
Shrine Island is more or less due north of Pirate Island, and shouldn't take too long to get to. You will probably run into a few random battles on your way, which is a good opportunity if you want to level up a little or earn a few magic experience.
Entering Shrine Island
When you land on Shrine Island, Aika will notice the gaping hole in the front of the small temple structure made by last night's Moon Stone crashing into the island. There's a save point here if you need it, and a long pathway across the water to the front door of the Shrine.
Once inside, you'll see the Moon Stone at the bottom of the Shrine - most of which is now underwater. You're given two options - swim down, or try something else. Since Aika can't swim, Vyse will decide to try to drain the water by opening the other doors around the temple.
Draining the water
First off, head up the steps to the right and around the border of the shrine. There's a door on the walkway directly above the entrance, which leads outside to a strange floating crystal. Once you activate it, the shrine starts to glow and will sink a little into the ground, preventing any more water from pouring into the area. Over to the right hand side of the temple there's a chest with "Sacri Crystal" x2 inside, and once you've gotten that head back in.
Follow the path around to the door you initially entered through, and go back through it. You'll now find yourself on a series of walkways around the bottom of Shrine Island. Follow those around to another door, and you'll notice water seeping out. Open that door, and water will pour out allowing you to enter the next level of the shrine.
There's another chest around here somewhere with "Moonberry" x1 in it.
Around to the left there's another chest, containing "Sacres Crystal" x2, and you'll also see another exit door over on the right. Outside, again follow the pathways around to another door by a save point - it's a good idea to heal everybody up here. Open that door to drain the last of the water from the shrine, and head in to grab the Moon Stone.
Unfortunately, it's not going to be that easy - a strange set of stones begin assembling themselves into what looks like a robot.
With The Sentinel out of the way, you're free to take the Raw Moon Stone home - Vyse and Aika will celebrate their victory, and head back towards their boat.
Meanwhile
Back at Pirate Isle, Ben the Lookout is about to start his shift with some stretches when he notices a fleet of Valuan ships on a direct course for the pirates' base. As the inhabitants flee incoming cannon fire, Valuan Admiral Lord Galcian watches the panic from the bridge of his ship and instructs his subordinate Ramirez to capture all the pirates - or destroy the entire island as an example if they refuse to cooperate.