Mermaid's Cave is a dungeon that you will have to visit in both time periods in order to complete. If you get stuck in one of the dungeons, go to the dungeon in the other time period to see if you make progress.
Get a Gasha Seed
Start by going to the dungeon in the past. Bomb the wall on the right and go through.
Kill all of the Wizzrobes here to reveal a chest that contains a Gasha Seed. Go to the next room.
Get the Dungeon Map
Use Ember Seeds on the Candleheads to open the door in the northeast corner. Go through.
Swim west to reach a chest that contains the Dungeon Map.
Move the Wall
Now swim east. Light the torches in this order:
1 2 4 3
The wall will move, revealing a patch of dark water. You can't swim in this, so just go back the way that you came until you reach the entrance.
Get the Compass
From the entrance, go north, then west. Jump over the tile in the center to reveal the Gels. Kill them. Jump over the center tile if the Gels turn invisible again. Open the chest to receive the Compass.
Get a Key
Go back out and go north until you can't go north anymore. Kill the Keese and Candleheads in this room (shoot the Candleheads with an Ember Seed) to open the door. Go through.
Jump over to the ledge on the right and kill the stalfos to reveal a chest. Open it to get a small key.
Bomb a Wall
Go back a couple of rooms and use the key on the locked door in the west wall. Go through.
Go to the upper-left corner of the room and get rid of all but the middle pot. Push it onto the left switch. Then use the cane of somaria to put a block on the switch on the right. Use the feather to jump to the north exit.
In the next room, kill the wizzrobes and wallmasters, then use bombs to blast through the blocks. Go to the north wall and put a bomb to the right of the center of the north wall. If you placed it correctly, it will break a hole in the north wall. If you can't find it, tap the north wall with the sword to hear where the wall can be bombed.
Leave the Dungeon and go to the Present
After bombing the wall in the room where you bombed the blocks out of the way, you won't be able to do anything more in this dungeon yet, so go outside and use the Tune of Currents to go to the present. Go into the cave and use the Mermaid Key to get into the dungeon here.
Get the Map
Go north from the entrance. Get past the Ropes and go north, then west. Use the Switch Hook on the stone diamond across the gap to reach a chest that contains the Dungeon Map.
Get a Second Key
Go back to the last room, then go north. Hit the crystal switch to change the floor. Go to the top right part of the room and hit the crystal switch again to get access to the door on the right. Go through.
Use your seed satchel to put a scent seed on the floor. The Ropes on the right will rush toward it, falling into the gap. A chest will appear that contains a small key.
Get the Compass
Go back to the entrance and go east, killing the Candleheads to reach a room with two Giant Blade Traps. Unlock the door in the top right and go through.
Use the switch hook to get across. Go east and open the chest to get the Compass.
Get a Third Key
Go north from the entrance to reach the room with the crystal switch in the center. Hit it to make the floor reachable, then go over to the bottom left corner of the room and hit the crystal switch again to access the door on the left. Go through.
Be careful of wallmasters and wizzrobes. Bomb the south wall between the two red blocks and go through.
Use the switch hook to get the stone diamond out of the way, then use the switch hook on the lower stone diamond and bomb the south wall. Go through.
Push the block down once and left twice onto the red tile. Then push it right twice, up, left, down, right, up, left, down, and all the way right onto the yellow tile. Then push it left twice, up, right, down, left, then all the way up onto the blue tile. This reveals a chest that contains a small key.
Get a Fourth Key
From where you got the last key, with the colorful block puzzle, go north to the room with wizzrobes and wallmasters. Get rid of the enemies, jump to the top part of the room, then go through the hole in the north wall to reach a room with two rotating devices. (If there is no hole in the wall, go back to the past and read the Bomb a Wall section up above.)
Use the first rotating device, then the second one. Go through the north exit. Jump down from the ledge to the right and exit south. Use the two rotating devices again and now you can use the southwest exit. Go around and get the small key from the chest.
Reach the Mini-Boss
From the chest, jump off the ledge to the right and follow the path back to the rotating device room. Use the top device and follow the path to the chest that you just opened. Jump down the ledge to the right of the chest and follow the path back to the rotating device room. Use the device, exit north, then jump off of the ledge to the right and exit south. Use the rotating device. You can go up some stairs and exit to the northeast. Go up the ledge and around to the locked door. Go through.
You will be attacked by Vire. This enemy is very easy. Hit its energy balls with your sword to get rid of them. Wait for Vire to charge toward you, then attack it. Hit it a few times like this and it will split into two bats. Wait for the bats to charge toward you and hit them.
Go through the door that opens on the right.
Get the Mermaid Suit
Throw a bomb at one of the cracked blocks such that it explodes before falling into the pit. Then use the switch hook on the stone diamond to reach the chest. Open it to get the Mermaid Suit. Now you can swim in deep water.
Get the Boss Key
Go back to Vire's room and use the warp point. Then go east and continue until you are in the easternmost room of the dungeon that you can reach. You have to swim differently now. Press the directional pad to swim around. Pressing A will not move you around now. Go down the stairs in the dungeon's easternmost room.
Jump across the blocks, then ride the platform to the right side of the room and go up the ladder. Use the southwest exit to reach 10 rupees in a chest. Then go back to the last room and unlock the key block and go through the northwest exit. Go to the next room.
The correct lever is truly random, so just keep pulling the same one until it makes the chest appear. Open it to get the Big Key.
Get a Ring
Exit this dungeon and dive into the deep water just outside of the dungeon entrance. Swim to the treasure chest and open it to get a ring.
Get a Fifth Key
Go outside and go to the past. Go into the dungeon. Go all the way east from the entrance to reach the deep water that you revealed when you lit the four torches. Dive into it.
Swim west. You can use any item equipped to A, so you can put your sword there to be able to attack enemies. Swim around to the stairs on the bottom right. Go down.
Swim right and go east, then go up the hole in the room on the far right. Swim against the current to use the northwest exit, then go through the exit at the top.
Kill the Ropes while avoiding the fireballs from the statues to reveal a chest that contains a small key.
Get a Sixth Key
Go back to the dungeon entrance and go north until you reach a room where some bubbles are going around the walls and there are some stairs to the right. Go through the door on the left side.
Use the Cane of Somaria to put a block onto the switch on the right. Kill the floating Wizzrobe, then go to the left side of the room and push one of the pots onto the switch on the left. You can also use the switch hook to bring a pot closer to you for pushing. Go through the door that you opened.
In this room, you should already have bombed the north wall. If not, read the bomb a wall section above. Go to the north wall and go through the hole.
Get into the rotating device, then go around and use it from the top. Go around and use it from the top a second time. Dive into the deep water.
Use the northwest exit to reach a chest that contains 30 rupees. Then go south and use the northeast exit, then exit to the right. Kill the Ropes while avoiding the fireball from the statue, then exit north.
Go around and kill the ropes while avoiding the spears from the north wall. Exit to the east. Use the switch hook to cover the brown area at the top with all six diamonds. Open the chest to receive a key.
Reach the Dungeon Boss
Go back to the room where you started in this watery area and go back to the surface. Use a small key on the locked door on the left.
Unlock the key block to the left. Step on the switch until the rotating barriers are vertical. Step off of the switch and use the Cane of Somaria to hold down the button so the rotating barriers are angled toward the crystal switch. Diagonally hit the block on the left that is just below the rotating barriers with a seed using the seed shooter to activate the crystal switch. Go across the bridge. Open the Boss Door.
To defeat Octogon, first stand on the platform in the center of the room and get rid of the two pots. Equip the seed shooter. When Octogon stops and turns around, it will spit a rock at you. Move so that you aren't in the direct path of Octogon's mouth, and shoot a seed at it when it spits a rock at you.
Eventually Octogon will be partly submerged. Get into the water and dive down. Equip your sword or another weapon to A and use it to hit Octogon repeatedly. Be sure to swim around a lot to prevent Octogon from hitting you. After hitting Octogon for a while, it will float back up. Go back to the surface and stand on the platform again to hit Octogon with the seed shooter as before. After hitting Octogon enough times, it will die.
Get the Bereft Peak
Go east to get the next Essence: Bereft Peak. The Maku Sprout will say that Ambi has left the palace, so you should go to Ambi's Palace to save Nayru.