Your map shows the red pendant at the top of the mountain to the north.

Go through the Cave

Go west from the Sanctuary until you see the pond with the whirlpool in it, then go north from there. Continue going north until you find a sign that says not to climb Death Mountain. Go east from the sign and lift the boulder, then throw the boulder and go east. Enter the cave.

Go north to jump down the ledge, and keep going north until the path splits. Go east at the split, then go southeast, then north through a narrow passage. When the path splits, go east and approach the old man. He will join you. Go east through the door.

Keep going east, and the old man will stop you when you approach a hole. Go east past the hole, and when the path splits, continue going east. When you approach another split in the path, the old man will speak to you again. Go south at the split, and continue along the path to go outside.

Find the Old Man's Shelter

Go east, and don't let the boulders hit you. Avoid the Deadrock enemies, which temporarily turn into stone if you hit them. If they are still moving around, you can sprinkle Magic Powder on them to turn them into Slimes, which can be defeated easily (but the falling boulders may make this difficult). Keep going east to find a doorway. The old man will speak to you once more. He gives you the Magic Mirror. Follow him into the cave, and you can talk to him to be fully healed.

Go up the stairs behind the old man, and go through the door. Go south (the pot in the corner just has one rupee under it), and follow the path to the next room. Follow the path, and go south whenever the path splits, to reach a door to the outside. Go through.

Go to the Top of the Mountain

Quickly go west, avoiding boulders, and go up the ladder. The boulders will stop. Go east, and you will find Spectacle Rock. Ignore the cave entrance into Spectacle Rock for now, and instead jump off of the ledge south of that cave entrance, staying on the left side of the ridge of rock. You will land on a small ledge with a door. Go inside, then keep going north to reach a room with a Piece of Heart. Take it, then go back the way you came, to reach the small ledge outside.

Drop down from the small ledge, then go west and climb up the ladder again. Go east and you will find a strange glowing tile in the middle of the circle. Step on it.

The world around you will change, and you will also change form. Go west, and you can optionally talk to the strange people here. The ground near them is a lighter color, and is the same shape as Spectacle Rock. Stand on the upper part of the lighter ground and use the Magic Mirror that the old man gave you. You will be sent back to the normal world, but now you will be on top of Spectacle Rock.

There will be a glowing spot where you appeared. This glowing spot will also appear on the map (press X). You can step into this glowing spot if you want to go back to the strange world, but there is nothing to do there now, so just ignore it. Get the Piece of Heart from the top of Spectacle Rock in the normal world, then go north and jump off of the ledge. Go east and you will find the Tower of Hera. Go inside.