The Slime Eel's head appears from four holes in the corners of his chamber while his tail swings around in the center. Stay in a corner to avoid being hit by the tail. Use the Hookshot to pull the head of the eel way out. If he's got a heart on his neck, it's the real eel. Attack him with the sword as much as possible. If there's no heart, he's an imposter. Don't attack that one. A few hits to the heart and he'll be gone.