After you use the whistle to get heart containers and other items, you should go to Dungeon 3.
Get Monster Bait
If you don't have 60 rupees, fight monsters until you do. Try fighting blue tektites in the south part of the map for a better chance of getting blue rupees.
You will need Monster Bait to get the treasure in the next dungeon. Various shops sell it, but you can get the best price (60 rupees) in the northeast corner of the map. To get there, use the whistle to warp to dungeon 1, then go east, then north, then east five times. Go north, then east twice. There is a secret passage north of the bottom-middle tree stump. Go up through the north wall there to find a hidden building. Go inside and get the monster bait for 60 rupees.
While you are here, look to see how many keys you have. If you have two or more, you don't have to buy any. But if you only have 1 key, you should buy one. (Go outside and back in to make the merchant reappear.) If you have zero keys, you will need to buy two. This shop has the best price for keys, so if you can't afford them now, just remember that this shop is in the northeast corner of the map, so come back here to get the keys you need if you can't proceed in a dungeon.
Or, if you can't afford the keys, you could go back to previous dungeons and get keys that you missed.
Go to the Dungeon
If you are at the shop where you got the monster bait for 60 rupees, go south, then west twice, then south three times, then west, and finally north. Use the whistle to reveal the dungeon 3 entrance, and go in.
If you are not in the northeast corner of the map, use the whistle to warp to dungeon 1, then go east, then north, then east five times. Then go south twice, then west, and finally north. Use the whistle to reveal the dungeon 3 entrance, and go in.
Go north twice. Kill the ropes to get bombs.
Get the Map
Go north and get the map. Kill the blue goriyas to open the door.
Get a Key
Go north and kill the Stalfos to get a key.
Get the Magic Boomerang
Go north and equip the monster bait, then press B to give it to the monster. Then go north through the locked door. Kill the Goriyas to get the Magic Boomerang, which goes much farther than the regular boomerang.
Go to the Dungeon Boss
Go south until you see a locked door to the east. Go through that locked door.
Put a bomb in the path of a Dodongo to make it eat the bomb. Wait for the bomb to explode in the Dodongo's stomach, then put another bomb in its path, and repeat this until each one is dead. Take the heart container that they leave behind.
Get the Compass
Go south through the locked door from the Dodongos's room. Carefully go into the center of the room, avoiding wallmasters that come out. Get the compass.
Get a Second Key
Then touch the wall to lure wallmasters out, then kill each one. After the wallmasters are all dead, push the middle block on the right side. Stairs will appear. Go down and follow the passage until you are upstairs again. Get the key from the right side of the room. Then kill the Goriyas. The door will open.
Get the Triforce Piece
Go north and get the Triforce Piece.