Instructions
Defeat the Eastern Palace and the Desert Palace, respectively. You'll get the Pegasus Boots in the Eastern Palace, which you'll use to reach and enter the Desert Palace. During the course of the Desert Palace level, you'll receive the Power Glove. This item allows you to lift the rocks that block the way to the Moon Pearl's location.
Go to Death Mountain, located to the north of the game's main island. Within this area, enter the Tower of Hera, where the Moon Pearl resides.
Go to the ground floor (GF) through the set of stairs to the north of the entrance. Defeat all the enemies present in the subsequent two rooms with ordinary sword attacks.
Press the "Start" button to access the Items menu and select the lamp. Light all four torches to summon a treasure chest in the middle of the room. Stand before it and press "A" to open it, granting you the Big Key. You need this key to open the chest containing the Moon Pearl.
Retrace your steps to the main entrance. Go up the stairs on the east side and defeat any enemies present. Proceed to the fourth floor (4F).
Step on the switch located directly to the south of the stairs you came from. The switch resembles a yellow star and is next to a rotating fireball. Once you step on it, it will turn off, eliminating its yellow color.
Drop into the hole revealed by the switch, located directly to the east and close to the center of the room. This will land your character back on the third floor. You'll land on a small, secluded area otherwise inaccessible from the third floor itself.
Open the treasure chest located directly above your landing position to obtain the Moon Pearl. Step on the switch to reveal a piece of ground that allows you to exit the isolated area. Proceed to the fourth floor to defeat the tower's boss using ordinary sword attacks.