After you get the instrument in Tail Cave, you learn that BowWow has been kidnapped. Your search leads to Goponga Swamp.
BowWow Kidnapped
Go north. The kids who were playing catch will run up to you and say that some Moblins went to BowWow's House. If you go there, you find that BowWow was kidnapped. Madam MeowMeow doesn't have any more information.
You have seen some Moblins in Mysterious Forest, and if you go to a phone building and talk to Ulrira, he says that the Moblins can be found in Mysterious Forest or Tal Tal Heights to the north.
Optional Rupees and Secret Seashells
In the Mysterious Forest, go east to where you can see a treasure chest beyond a rock that you can't lift. Go north from there until you can't go farther north, then go west, then north. In the Nintendo Switch version, if you have the Shovel, you can dig near the trees on the west side to find a Secret Seashell. (This Seashell is unavailable in the Game Boy version.) Jump over the holes in the ground. You can go into the house and talk to Mr. Write, but he doesn't have much to say at this point.
Go north from Mr. Write's house. There are worm-like creatures here called Like Likes that can steal your shield if they eat you, but you can avoid this by putting your shield into your inventory instead of assigning it to a button, and if they do steal your shield, just kill them to get it back. If you leave the area before getting the shield back, you can buy another one from the shop in Mabe Village.
Keep going north from Mr. Write's house and enter the cave, then use the Roc's Feather to jump over the gap and reach the treasure chest. It contains 20 rupees.
If you are playing the Nintendo Switch version and you have the shovel, go outside and go east, and cut the rightmost bush and dig under where it was to find a Secret Seashell. (This Seashell is unavailable in the Game Boy version.)
Then go southwest to return to the Mysterious Forest, and go east until you reach the place with the Piece of Heart in the middle of the holes.
Optional: Visit the Camera Shop/Dampé's Shack
If you didn't get the optional items mentioned above, go northeast through the Mysterious Forest until you reach the place with the Piece of Heart in the middle of the holes. Jump to the Piece of Heart, then jump north to a path that you couldn't reach before.
Go northeast and you will see an owl statue next to a cave entrance. You can optionally go east, and in the Game Boy version, you will reach the Camera Shop, where you can get your picture taken and unlock the photo feature of the game; in the Nintendo Switch version, you will reach Dampé's Shack, where you can create custom dungeons.
If you are playing the Game Boy version and want to get more photos now, you can get "(Link) Discovers Ulrira's Secret" and, if you haven't stolen anything from the shop, you can get the "Thief!" photo if you don't mind being renamed THIEF and not being able to go back into the shop for the rest of the game.
(Switch Version Exclusive) Optional Piece of Heart and Secret Seashell
If you are playing the Nintendo Switch version of the game, there is a Piece of Heart that you can get now, and if you have the Shovel, there is also a Secret Seashell that you can get. Go east from the cave with the owl statue next to it, then go south from the sign, to find Tabahl Wasteland. In the east side of the area, dig in the dirt on the east side to find a Secret Seashell. There is also a Piece of Heart that you can jump to in this area.
Enter the Moblin Hideout
Go into the cave with the owl statue next to it. This is the Moblin hideout. Fight the Moblins and go through the cave. You will find King Moblin.
King Moblin
Avoid King Moblin's spears and allow him to come closer to you. After a moment, King Moblin will wave his arms, then charge toward you. Step out of the way so that King Moblin crashes into the wall. Hit King Moblin while he is stunned. Repeat the process until he dies.
Find the Next Dungeon
Afterward, go east to find BowWow. In the Game Boy version, touch the rock that he is attached to. In the Nintendo Switch version, check on BowWow. You will carry him with you. Leave the cave and go west, then south. Jump over the holes in the ground and go west. Continue going west through the forest until you can go north. BowWow might sometimes eat your enemies for you. Then in the area with the house on the other side of the holes in the ground (Mr. Write's house), go east until you reach the swamp, then go north.
Stand near the Goponga Flowers in the path and wait for BowWow to eat them. Then go east. In the area with a large Goponga Flower and a Piranha swimming in the water, use the southeast exit. Wait for BowWow to eat the large Goponga Flower in the way, then go east to find a chest that contains 50 rupees.
Go to the northeast part of the swamp to reach a cave entrance that is blocked by more flowers. Wait for BowWow to eat them, then go into the cave. This is the second dungeon: Bottle Grotto.