Walk up to the middle statue to use the key you found in the forest. This will open the way for you to enter the dungeon. From the entrance go left and you will see two beetle-like enemies. Use your sword to knock them off the edge and you will get a key. Continue left and you will be in a room with four jelly-like monsters. Kill them with your sword to open the door that closed behind you and then collect the compass from the treasure chest. The compass will sound when you enter a room with a key, making them easier to find.
Now, backtrack to the entrance. Go up and you will be in a room with two mini-jellies and a beetle. The mini-jellies can't hurt you but they can latch on to you and slow you down. Kill them with your sword and knock the beetle down into a hole. Step on the button to reveal a treasure chest containing a key.
From there, go right and defeat all the enemies for a key. Walk up to the person-shaped portion of the wall which will swing you to the next room. There isn't much to do here so head right. From this room, go up and you will see three enemies with playing card suits on them. When you hit them with your sword they stay at the suit they are currently showing. Freeze them all at the same suit for a treasure chest containing a beak. This allows the owl statues to give you advice.
Backtrack two rooms and this time head for the left room. Inside of the chest in this room is a key. You have to be quick because of the sun moving around it. You will be able to defeat these when you have the boomerang, but that is much later in the game. Continue left, because going up leads to a dead end.
In this room you will see a cracked wall, if you have bombs already you can bomb that area and in the room it leads to, receive a shell. Otherwise, just defeat the monster to receive 50 rupees. You can break the crystals with your sword to go down but that just leads to somewhere you've already been. Go upwards instead.
In this room, you see a blade that will slide towards you if you try to go for the next room. Push the block into its way so that it can't slide at you when you try to cross.
From here, you have to zig-zag a little bit. Continue along the narrow walkway while avoiding the suns. Eventually you will come to a closed door. Push the leftmost block right to open it, keeping in mind that the sun will start orbitting the block once you've pushed it.
Now you will find yourself in a room with two spiked monsters. Let them ram into you when you have your shield up to flip them over and attack the underbelly with your sword. You can now descend the staircase that appears.
You are now in sort of platformer environment. You can see goombas moving at the bottom. Simply walk off the left ledge to fall to the next and walk off that and climb the ladder you fall near. Just keep doing this while working your way across and you'll eventually come up in another room. From this room, go up and you will see a flying heart. You can get this soon. Go up again and while avoiding the sliding blades, grab the treasure chest for the Roc's Feather, which allows you to jump.
You'll have to head back a fair bit now. Go back to the room just before the one with a bombable wall. Take the upper right way out. Continue along until you come to a room with a beetle. Knock him down the hole and jump across. Use a key on the block and continue to get the Nightmare Key. Now go back to the room just before the one where you got the beak. Jump across the hole and be ready for a mini-boss.
He will roll what looks like a giant hair curler at you and you simply need to jump over and slash at him as he works his way across the room. It shouldn't take long to wear him down. Your health will be fully restored upon defeating him and a teleporter will appear allowing you to go back to the entrance if you so desire.
Continue up to the next room. Be careful not to get hit by the sliding blades that will attack anything near the edge of the room. Don't bother going down the stairs, they are only needed if the Nightmare knocks you down.
The Nightmare is fairly straight foward. If he knocks you down a hole, you can just work your way along and come up at the staircase before you fought him. However, his health will be refilled again if this is the case. To damage him, simply attack the sparkling end of his tail. After about four hits from your sword he will fall. Collect the heart container he drops and then go on to collect Full Moon Cello.
And that's it, you've completed Tail Cave.