If you talked to the guy in the former thieves' hideout in Kakariko Village, you heard the tale of Blind the Thief, who hated bright light. Keep that in mind...
Enter the Hideout
Drop down the ledge in front of you, careful to avoid the Daira, and lift the skull above. Walk north and you'll see a fireball circling a statue, and a couple more Daira. The red one will spit fire at you if it sees you, so be careful to avoid it. Go left under the walkway to find the chest containing the map. Then walk back to where the statue-circling fireball is, and walk north of it, under a walkway, to the next room.
The chest on the walkway above is just a red rupee. Stay on the lower area, and make your way around to the far right of the room, where you should exit to the next room. (There are two east exits; a red Daira is hanging out by the bottom-right one.)
Once you're in the next room, go to the very bottom of this room and use the leftmost exit in the south wall. (You're likely to encounter a swirling yellow thing; if it touches you, it will temporarily counter the effects of the Moon Pearl, and you turn back into a pink bunny for a few minutes, unable to use weapons or items. Try to avoid these if you see it coming.)
In the next room, go up the stairs below and go around to the compass. From the chest, drop down off the left side of the walkway and continue left to the next room, where you find the chest containing the Big Key. Go back to the last room, then go to the very top of this room and use a north exit.
Go up the stairs and head to the north wall to find a big key door. Go through it. Head to the top of this room, fighting stalfos on the way, and lift the top-right skull to find a small key. Go back to the bottom of the room and use the key in the bottom-left door. Fighting the daira and avoiding the flame snake, go through the west door to the next room.
The only vulnerable part of the amoeba-like clouds is the small amoeba that comes out of it. Get past the clouds and the bubble, carefully crossing the conveyor belts, to exit west.
Make your way north against the conveyor belt, fighting enemies, and exit through the north door.
Careful of the Zol that will pop out of the floor. Pick up the skull to find a key, then from a safe spot, hit the crystal switch, releasing the spike traps (make sure they don't hit you after you release them). If you don't want to deal with them, try hitting the crystal switch a couple more times until all the traps are on the other side of the orange blocks. Either way, with the orange blocks up, get past the traps to unlock the north door and go up the stairs.
Don't pull the lever; it just drops skull ropes. Instead, lift the bottom-right pot to reveal a switch. Step on it to go to the next room.
In this corridor, kill any green monsters that get in your way and head east until you get to a room with a single window with light shining in. Leave the chest alone for now, and kill all the green monsters. The floor where the light is shining is cracked, so stand a distance away from the cracks (between the tables is good), drop a bomb, then press A to pick it up, and press A again to throw it onto the cracked part of the floor so it blows it open, letting the light shine through to the floor below. With that done, grab the bombs from the chest and leave.
It's a straight path to the long conveyor belt, but to get past the spike traps you will probably have to hit the crystal switch. Just make sure that when you leave, the blue blocks are down. In the conveyor belt room, go past where the blue block was and through the top-right door.
Get past the dairas and cloud to exit east, then in the room full of conveyor belts, make your way to the stairs in the north wall, and go down. Kill all the enemies in here (throwing skulls is effective), and go through the door that opens.
Make your way south down the conveyor belt, careful of Zol that appears and trying not to get pushed off the sides. The hookshot is effective against the Bari. Once at the bottom of the room, exit right. Use the east exit here to reach a jail. The big key opens these doors, so go north through them and you find... one of the seven maidens..? But weren't they all entrapped in crystals? (Furthermore, wouldn't she have been transformed by the Dark World's power?) Talk to her, and she asks you to lead her out of the dungeon. She will follow you from now on. Open the chest next to her for a small key, then exit the way you came in.
Go straight across back to the room with the long conveyor belt, and walk right across it and unlock the west door. Be warned: In a few moments the floor around the big chest will crumble. Use your hammer on the pink things to reach the big chest, quickly open it and run out of the room before you get trapped in the center. Now you have the Titan's Mitt, which allows you to (finally) pick up black stones and other objects that were previously too heavy to lift.
Go east across the conveyor belt again, to the last room with the red daira and small conveyor belt above. Go through the north door and you reach the room with the very big block. Now that you have the Titan's Mitt, you can pick it up, so do that and get rid of it. Go up the stairs to the room with all the conveyor belts.
Lift the top-right skull to find a switch; step on it. The east door will open, so go through it. Now exit through the north door, and you find yourself in the room where the light is shining through the hole you bombed open above.
Now, think for a minute. This is Blind's Hideout, right? So where's Blind?
Right behind you!
Blind hates the light, so walk the girl into the light and she screams in pain, transforming into the Dark World version of Blind, a huge, white-robed beast with an ugly red head.
Blind the Thief
Blind will move side to side at the top of the room. Occasionally he will stop for a second and shoot a laser from his eyes in the direction he's facing, so be careful not to be in his line of sight when he stops. Eventually he will move to the bottom of the room, moving side to side. This is your chance. Hit his head with your sword, and he will spit fireballs in every direction for a few seconds. Try to avoid them. After you hit his head three times, it pops right off and starts flying around the room, spitting a fireball every few seconds. A new head will grow, and Blind will repeat the aforementioned pattern. Avoid the random fireballs as best you can, hitting Blind's head until THIS one comes off and starts flying around the room spitting fireballs. Two heads will be floating around, both spitting random fireballs, and you will have to hit Blind's third head until he dies. You will probably be needing the fairies you hopefully have in your bottles. If you're really having trouble, you can try to use the Magic Cape to avoid attacks every once in a while. Good luck!
Once the beast is slain, walk into the explosion to claim the heart container, then move to the center of the room to catch the crystal.