THROUGH THE WEB
After getting the Fairy Slingshot, equip it and look towards the door you came in. The ledge is too far to be able to climb up, and you're not able to jump to it. However, there's a ladder above the door that you can shoot down, so target it and fire your Slingshot to knock it down.
Go through the door and the next one to get back in the first room. The Skullwalltulas that were blocking your way previously can now be killed with the Slingshot, so do that and climb the vines. It doesn't matter which side you get off, so get off and then go to the door.
In this room, there is a chest on the opposite platform and a switch when you first walk in. Stepping on this switch will raise three platforms in the room, so do that and go across to the chest, which contains the Compass for this dungeon. Every dungeon has a Compass, which will reveal treasure chests, the boss door and Link's current location.
Once you have the Compass, go to the ground and go towards the alcove, which will make a Skulltula drop from the ceiling. These are armored on the front, but will turn around, exposing their weak spots. It takes two hits from your sword to kill it (one Jump Attack). Once it's dead, go back to the switch and hit it, then use the platforms to get to the alcove. The chest only has a Recovery Heart, but you came over here for the Gold Skulltula, so kill it and collect its token.
To get back to the main room, go to where the switch is and take out a Deku Stick. Light it with the torch, then light the unlit torch, which will open the door. Back in the main room, go towards one the nearby ledges and a Skulltula will drop, so take it out in the same way. What you want to do is get a running start and hop off the ledge, aiming for the web down below, which if done right will break and allow you into the area below.
There are 2 Gold Skulltulas in this room, so grab them. There is a platform with a switch, which will ignite the torch nearby. Light a Deku Stick and make sure you hop into the shallow water, as the deeper water will put out the fire on your Deku Stick. Hop across to where you see the Deku Baba and burn the web there.
There's another Deku Scrub in this room and once you defeat it, it will reveal a clue about defeating his brothers in the proper order later on in the dungeon (2-3-1 is the correct order). To get into the next room, shoot the eye above the door with your Slingshot, then go through the door.
In this room, there is a platform going back and forth across the water, with a spiked log in the middle. If you jump on the platform now, you will hit the spiked log. Hop into the water and go to the far left, underneath the log. Dive and you'll hit a switch, which will lower the water level.
This is timed, so hurry back to the previous platform and then hop on the moving one. Once you pass the spiked log, jump onto the next platform and kill the Skulltula. Grab the block, then drag it over enough so you can use it to climb up and go through the next door. Iron bars will block the doors, so kill the Deku Baba, then use a Deku Stick to light the two torches to open the door.
Before you move too far in this next room, use your Slingshot to kill the Skulltula, since it's already turned around. In the middle of the room, you can see three shadows on the ground, which when passed over, will drop three eggs that spawn Gohma Larvae. These take two sword hits (one Jump Attack) to kill, and all they do is lunge at you, which happens when their eye turns red.
Once they're all dead, use a Deku Stick to burn the web in the little hallway (the other leads to a Gold Skulltula, but you can't get it now). Crawl through the small tunnel and you'll emerge in a room with more web on the ground. The torch nearby is too high, so push the block off the ledge and into the lower portion, then light a Deku Stick with the other torch below. Using the block, get back up to the higher ground and roll over the web.
Drop down into the hole and you'll land in some water. Get onto land and you'll be faced with three Deku Scrubs. If you remember the clue from before, you'll know that the order to defeat them is 2-3-1. Target the middle one, bounce the nut back, then do the same with the one on the right, then the one on the left last. They offer a tip for fighting Queen Gohma and the door will open, leading the way to the boss.