The Elder of Seaside Town—where everyone is acting strangely—tells you to get the Star Piece for him.
Cross the Sea
Go southwest to the next room, then go southwest to find a cloaked figure. Talk to it and you can purchase goods from the shop.
You can optionally go west of the cloaked figure and go southwest to a room with a Save Block. Then go northeast to the room with the cloaked figure, and this time go southeast. There is an exit near the southern corner of the room that leads to a new area.
Go southwest past the crates, then hit the treasure chest to get an invincibility star. Go southwest to the next room and if you're still invincible, you can quickly defeat all the Zeostars on the floor as you go west. At the west corner of the room, go through the northeast door (which is a bit difficult to see), jump on the crates, then go to the northeastern chests first to get a flower and Frog Coin, then open the southwest chest to get a mushroom. Then go southwest again to return to the previous room. From there, go southwest to the next area.
Jump into the water and swim into the whirlpool. Then walk northeast, and go through the door in the west wall (also a bit difficult to see). Go northwest to stand in the bubbles, then jump out of the water and open the chest to get a Max Mushroom.
Jump down to the area below, and go southwest to the next area. Get into the water and swim into the whirlpool, then go west to find the Sunken Ship. Jump up onto the sails, then stand on the crow's nest (the round thing on top of the sails), and press Down to enter the Sunken Ship.