The Magic Hammer gives you access to much more of the Dark World, allowing you to collect a number of treasures before you proceed to the next dungeon.
Get a Piece of Heart
From the Palace of Darkness, go west through the large hedge maze where you met Kiki the Monkey, then go west through the narrow hedge, go south and then east through the narrow hedge there, go east past the building, and go south through the hedge maze between the two arrows, and finally, go southwest to exit the area.
Go west from there, and you will find a bridge to the south that is blocked by a number of purple posts. Use the Magic Hammer to get these posts out of your way. This gives you access to most of the rest of the Dark World.
Go west and you will find the Bomb Shop in the location where Link's house is in the Light World. You can ignore the shop for now (unless you need bombs), and go west, then south, then west again. You will find some trees with eyes. If you touch their mouths, they will spit out a bomb, and you can then talk to the tree, which might yell at you or might give you advice.
In the west side of this area, there is an arrow of bushes pointing south. Go south from the arrow and you will find an area with a circle of bushes. Cut one of the bushes and go inside of the circle, then use the Magic Mirror to go to the Light World. Enter the cave, lift the pots, and collect the Piece of Heart.
Get the Shovel
Go back outside and step into the sparkling spot to return to the Dark World. Go north and cut through the bushes that are in the shape of an arrow, and go north from there to enter a forest clearing. Go north and talk to the person on the tree stump. Agree to look for the flute and you will get the Shovel.
Get the Flute
Go to the north end of the forest clearing and use the Magic Mirror to go to the Light World. Then go to the flowers in the northwest of the clearing and use the shovel to dig up the flowers. You will find the Flute, which replaces the Shovel.
Get a Second Piece of Heart
Step into the sparkling spot to return to the Dark World. Talk to the person on the tree stump again, then use the Flute. After the cutscene, go south to leave the clearing, then cut through the bushes and go northwest to where Kakariko Village is in the Light World.
There is an archery game here, and a digging game to the west. Play the digging game for 80 rupees (you will use the shovel during the digging game when you press Y, no matter which item you have equipped) and dig as many times as you can for a chance to find a Piece of Heart. You have to dig a minimum of 25 times (or just 20 times in the European version) for a chance to find it. Note that you can only dig to the left or to the right, not up or down.
Awaken the Bird
Go south from the digging game and use the Magic Mirror to return to the Light World. Go into Kakariko Village. You can optionally go into the building west of the southeast entrance of the village, and go to the nodding man. Play the Flute for him, and he tells you to play the Flute for the bird in the village square. Go to the weathervane in the center of town and play the Flute in front of it. A bird comes out and flies away. Now, whenever you play the Flute, the bird will fly to you and pick you up, and you can select a numbered location on the map using the directional pad. Then youc an press A to go to the highlighted location.
Get the Ether Medallion
Use the Flute and go to 1, on Death Mountain. Go east and enter the old man's cave, and go up the stairs and through the east door. Go southeast and go through the east door, then go south until you find the door to the outside in the south wall. Go through.
Stay near the north cliff as you go west, then go up the ladder. Go east and use the warp tile to go to the Dark World, then go west and stand on the lighter ground, and use the Magic Mirror to reach the top of Spectacle Rock in the Light World. Jump off of the north edge of Spectacle Rock and go northeast to find a bridge that goes west from the Tower of Hera. Cross the bridge, then use the Book of Mudora to read the inscription on the tablet. You will automatically raise the Master Sword and you will receive the Ether Medallion. You can use it to cast a wind attack that kills most enemies on the screen. It uses a lot of magic to cast the spell.
Get the Bombos Medallion
Play the Flute and choose 4 to go to your house. From there, go north and go through the castle gate to be sent back to the Dark World. Go east, then south until you reach the bridge with purple posts. Use the Hammer on the posts, go south past them, and go west to where your house is in the Light World. Go south from there to enter the swamp, then go southwest to reach the Swamp of Evil, where the desert is in the Light World. Go as far west as you can go, into an area bordered by purple posts. Use the Magic Mirror here, and you will appear on top of a cliff in the Light World. Go west and use the Book of Mudora to read the inscription, and you will get the Bombos Medallion, which hits all enemies on screen with an explosion attack. It uses a lot of magic to cast the spell.
Open the Next Dungeon
Go east and step into the sparkling spot to return to the Dark World. Go east until you find a building. Go inside to enter the Swamp Palace.