Slime Eye is the boss of the third dungeon of Zelda: Link's Awakening, the Key Cavern.
While the Slime Eye is less skill-based than other bosses, each phase requires a specific trick - most making use of your newly acquired Pegasus Boots - in order to defeat it.
If you're looking for more assistance, our Zelda: Link's Awakening walkthrough can help.
Slime Eye boss strategy
This boss has three phases. The first sees the boss hidden from view - unless you count the shadow in the middle of the room, that is - and you need to dash into a side wall to shake it loose.
Next, it'll passively bounce around the room. To damage it, you need to hit the eye with your sword from below. Doing so will cause it to split.
Keep damaging until it is almost ready to split, then dash through the middle of the boss with your Pegasus Boots.
The final phase has the split boss bounce around the room. Watch the shadows to see where it's about to land, then hit away at the eye from below using your sword. We'd avoid dashing here to avoid being hit - as if you collide into the wall, you'll fall over and be susceptible to attack.
Our Zelda: Link's Awakening walkthrough and guide can help you with the critical path, including the Eagle's Tower and Turtle Rock dungeons. There's plenty to be done on the side, too - including Zelda Link's Awakening Heart Pieces, Zelda Secret Seashells and the Zelda Link's Awakening trading sequence. Finally, there's also the new Zelda Chamber Dungeons feature to unlock and complete.
If you have a lot of health left, you can be risky here and try attacking when you can, but otherwise take it slow, as the Slimes could alternate their attacks, leaving you open when you have an opening on the other one.
After a few hits on both, the boss is done for. Now collect the third full Heart Container, and grab the Sea Lily's Bell from the next room.