Heart Piece #1
Location: Light World
One of the first Heart Pieces you will be able to get is in southern Hyrule, in the tall grasses. You will find a building at the very south of Hyrule and inside of it is a lever (it's the one to the right) to open the dam. When you open the dam, all the water around the building will be gone, exposing a Heart Piece.

Heart Piece #2
Location: Kakariko Village
Go to the northwestern part of Kakariko, where you see the cave and hole. Jump into the hole, and inside, use the bombs to blow up the secret passage and waiting for you inside of a treasure chest is a Heart Piece!

Heart Piece #3
Location: Kakariko Village
Beat the Maze Game in under fifteen seconds and you will win the Heart Piece towards the end.

Heart Piece #4
Location: Desert
Go to the northeastern part of the Desert, where you will find a cave. Follow the path inside and towards the south of the room where you will find an elder, is a cracked wall. Use a bomb to blow it up.

Heart Piece #5
Location: Light World
Near the left of the Sanctuary, you will notice that a block of stones are piled on top of each other. Use the Pegasus Boots to shatter them and reveal a stairway!

Heart Piece #6
Location: Desert
During the interlude of the Desert Palace, when you step out of the dungeon, there will be a heart piece waiting for you at the end of the cliff, right by a Vulture.

Heart Piece #7
Location: Death Mountain
Just after you walk up the long stair case to the top of Death Mountain (past the falling rocks), continue your way right until you see a cave. Directly below that cave is a brown rock, and below that is a ledge. Walk to the left of the rock and jump off the cliff. You will end up on a new ledge, where you can enter another cave. In this cave is another Heart Piece.

Heart Piece #8
Location: Death Mountain
When you take a trip up to Death Mountain, and teleport to the Dark World for the first time, you will notice two diamond shapes in the grass towards the immediate left. Step in between both of them, use the Magic Mirror to return to the Light World and a Heart Piece will be at your side!