Ignore the first shutter, instead bombing to the right. Make your way east until you encounter a Gleeok, defeat it, and then head north. If you press south, you will encounter a difficult battle with a Gohma (since you cannot access the bottom half of the screen, you have to shoot at point-blank range). This will only win you the Compass, so if you don't mind having a gap in your inventory feel free to skip.
If you listened to me and skipped Gohma, you'll be in a room with three Like Likes and an assortment of Wizzrobes. Clear the room for a key, and then SCOUR EVERY BRICK until one of them moves. This will reveal a secret staircase.
Taking the staircase leads you to a room with a Manhandla. Don't bother fighting it yet, instead walk through the south wall to enter a room with Wizzrobes. Kill them for another key (you should have three at this point) and bomb the south wall again to find a room with--you guessed it--more Wizzrobes. Kill these as well and push around on the bricks to discover DUN DUN DUN! The Magic Wand! (Feel free to use your potion as necessary; there will be an opportunity to leave the dungeon after this gauntlet, so you can buy a new one).
Make your way back north to the Manhandla, kill it, and go through the shutter. This is a one-way trip, which is why we wanted to head south first (Trust me, you do NOT want to run through this area multiple times). You'll be in a room with lava and more wizzrobes. Rather than fight them, head north through a pass-through wall and kill the enemies their to acquire the Red Candle. This concludes item collection for the dungeon.
Doubling back south (into the room with wizzrobes and lava), clear the room and head to the RIGHT (Right is the way out of this gauntlet, Left is actually an alternate entrance to this area we avoided by skipping that first shutter). You'll be in a room shaped like a key, crawling with Like Likes. Clear them out and push on the keyhole to reveal a staircase, then take the resulting passageway.
If you look at your map, you'll notice you're in a room right next to the dungeon entrance. This room has two exits, one to the north and one to the west. Take the north exit first and kill all the bats to grab another key (That makes four), then double back and use the west exit to return to the entrance. If you've used any potions at this point, you'll want to leave the dungeon to replenish them.
Either way, you're back at the entrance. Follow the same path you took in the first place, through the Gleeok Pen and into the room with the Like Likes. This time, though, head east. You'll find a room with a DigDogger; waste it and go to the north (South is a dead end). Here, dear old Abei will threaten to take one of your Heart Containers, so pay him the fifty rupees and head to the West (If you go North, you will find the map but end up back in the gauntlet where you found the Red Candle, and then back at start. Since I'm giving directions, it's not really worth it to sidetrack for the map).
If you listened to me and went West, you'll be in a room with a narrow hall, filled with Like Likes. Clear this room and look around the top half for a brick that can be pushed. This will give you access to the North wall, which should be bombed to proceed (If you continue west, you will end up in a very deadly room [which was hiding behind that first shutter] that leads to... that's right! The Gauntlet!).
You'll find yourself in a room with two Lanmolas. Clear them out for yet another key, then head west. The next room has a shutter and a key door; take the key door. This leads to a room with locks on both sides; ignore them and bomb the north wall. Ignore the Manhandla and bomb the east wall. Clear this room to find--YES! Another key. Head back to the room with the two locked doors and go to the East (The west is a trap leading back to the gauntlet). The remainder of the dungeon is fairly linear: just make sure you don't take any southward doors and push on the blocks when you have cleared the rooms. In the dead-end you'll inevitably encounter there is a push-block that must be pushed from the bottom to grant access to a passageway (any other direction will cause the block to be in your way. If you've pushed the block on top of another block, you've done it correctly).
You'll find yourself in a new combat stretch, with South serving as the only available direction to go. You'll need to defeat the enemies in each of these rooms (including a half-screen Gohma which will pose a significant challenge), then push a brick to reveal yet another staircase. If you've survived this nightmare, you'll appear in a familiar dark room in an unusual spot. It's that first hallway with the bats. With nowhere else to go, press against the north wall to pass through. This room has three sword-restoring blue bubbles; an omen for what is to come. Take the passageway and cringe as you are forced to lose the use of your sword. Proceed west to face the boss and finish the dungeon.