Before you leave the shrine, the imp spirit thing will stop you and give you a little present, a fragment detector! This device will appear in the top left corner of your touchscreen and will flash whenever you are in the vicinity of a tablet fragment, with it increasing in frequency the closer you get to it. Leave the shrine to automatically be taken back to Pilchard Bay, where you should speak with your mother.
It appears that a whole new island has been found near your island, with your father and the mayor heading to the castle to talk about it. So, you should follow and head to the castle in Estard yourself. As you arrive at the castle, you will see that the drawridge has been raised and if you talk to the right guard, he mentions that the Prince has gone to see Dermot the Hermit, so head there next. Kiefer is standing outside of his house, so talk to him and he says to meet with him at Shoreside Shrine.
If you happen to not know where this is, it's the temple structure slightly southwest of Pilchard Bay on the overworld map. Break through the pots and barrels (you can find a total of 3 gold coins and a Medicinal Herb if you want to break them all), then talk to Kiefer and Maribel. Take the hidden stairs and follow the path to find a boat waiting for you. When you're ready to depart, tell Kiefer and you will set sail.
Your objective is the white island located to the north of Pilchard Bay, so go around either side. Note that despite being on a ship, you will still get into random battles, so be ready to fight a few battles on the way to Ballymolloy. Land anywhere you want on the island and make your way to the village. As you set foot inside, you will notice that the fragment detector will start blinking, meaning there is a tablet fragment here.
Ignore that for now and go to the house in the northwest corner of the village, but don't go inside. Instead, break the pots just outside of it to get 25 gold coins . On the right side of the inn are two barrels, one of which contains a Seed of Agility . In the small house in the center of the village, you will find a Leather Hat in one of the cupboards. The last destination is the big house, so head inside and go to the third floor to find an Antidotal Herb in one of the pots. The man on the second floor, should you talk to him, will hand over a Green Fragment .
Exit the village and run to the Rainbow Mines, smashing the barrels outside for 13 gold coins and an Antidotal Herb . Talk to the man guarding the entrance, then head inside. In the northwest corner of the first area, you will find a Seed of Magic in one of the barrels. You might have noticed that there are no monsters in the mines, which is true to all but the bottom two floors, as you will undoubtedly see, but all of the monsters are the same as in the past version of the mines.
There is one thing that is different about the mines, though, which are the gem puzzles. For the first puzzle, get rid of the red and blue gems first, then push the top yellow one left, then push the other yellow one up to move on. The second one is a bit more confusing, but push the first red one north without it touching the other, then push it to the right to get rid of the red one there. From there, move the leftmost blue gem one spot to the right, then one down and all the way to the right, opening the way to the next floor.
The third puzzle is another one where it's easy to screw up (reset by changing floors). Push the blue gem one space to the left, then move the second yellow gem left. The next move should clear the path to the stairs, which is to push the yellow gem to the left of the ones you've cleared. The fourth, and final, puzzle is simple. Go to the bottom left corner of the room and push the red one there all the way north, then move the red one nearby to the right. You can now go around to the east side and move the blue one in the middle to gain access to the stairs.
It is on the next floor that you will encounter monsters now, with there being all of the same ones as in the past, including those from The Tower. You should see the stairs leading down from where you entered, so go around and take them to come to a four-way intersection with some more gems. As you can tell from the detector, the tablet fragment is here, but you don't know which path. You need to push the blue gem in the middle to one of the paths to unblock it, then move one more gem to unblock the rest of the path. Fortunate for you, there's only one path that has anything, which is the northern one, housing the Red Fragment .
Grab it and return to the castle in Estard, talking to the guard on the left to open the drawbridge. This is where things are a little confusing, as you can't go to meet with your father, and there's not much of an indication on what to do. Speaking with a few people inside of the castle reveals that Dermot stormed out of the meeting and is still in the castle somewhere, so it's time to try and find him. On the second floor, take the southern doors to go outside and find the single door on the eastern side of the castle out there.
Go through this door and down all of the stairs to find Dermot arguing with a guard. Talk to the guard to have him open the door, then follow Dermot to the basement, where he meets with his friend. Speak with Dermot, then talk with his friend to gain access to the raft, which you can board with the A button. Use this to go outside and to the western side of the castle, to some stairs. Get off the raft, ignore the stairs nearby and go to the northern side of the castle, where there will be a slightly hidden door underneath the princess' balcony. This will lead to a room with another Red Fragment , as well as a Seed of Agility in one of the vases. Return to Dermot to show him the tablet piece, then it's on your way to the Shrine of Mysteries once more...