Upon entering the room, Slime Eye will taunt Link, saying that he can't be found. Instead of fighting the boss, numerous green Zol will fall from the ceiling to attack Link. Link must use his Pegasus Boots to reveal Slime Eye by ramming the back wall at full speed. This will bring down Slime Eye from his hiding place on the ceiling. Once Slime Eye appears, using the Pegasus Boots in combination with his Sword, Link must perform a Dash Attack and split the gigantic eye into two (like a red Zol), and then slash the individual eyes to death. This gets Link the Sea Lily's Bell.
This boss resembles Vitreous, and the way the Zol fall from the ceiling may be a reference to Zol falling from the ceiling in the floor beneath Vitreous in A Link to the Past.
The concept of a boss hiding on the ceiling before the battle begins is later used by Gohma, Wart and the Deku Toad, among others.
Slime Eye splitting into two
Link facing Slime Eye
↑"SLIME EYE Dash against the wall to make it appear. Attack the eye, forcing it to split in two, then attack each eye separately with your Sword." (The Legend of Zelda: Link's Awakening Nintendo Player's Guide (Nintendo of America Inc.), pg. 103)
↑"The Nightmare that lurks in the Key Cavern is called Slime Eyes." (The Legend of Zelda: Link's Awakening Nintendo Player's Guide (Nintendo of America Inc.), pg. 45)