The eye is Morpheel's weak spot in the first phase of the battle. It moves around through the various tentacles, but can be Z-targeted. Pull out the Clawshot and pull the eyeball out of the tentacle. With the Iron Boots also equipped, just slash at the eyeball so it then returns to Morpheel's body.
Try not to stand in a single place since Morpheel uses its tentacles to grab Link and then toss him into its mouth. It then spits Link out, so immediately remove the Iron Boots and swim away; otherwise, Link falls right back into its mouth. Link can swing at Morpheel's tentacles when they try to grab him to make them retract. Morpheel also tosses Bombfish towards Link. Striking them with the Sword activates the Bombfish, so quickly swim away or toss them to the side.
Repeat the process of pulling the eye out and slashing it with the Sword a few times until the first phase of the battle is complete.
Morpheel then comes out from underground and reveals its entire gigantic body. The weak spot is now the eye on top of its head. Un-equip the Iron Boots and swim after Morpheel. Once Link is close enough, Z-target its eye. Use the Clawshot so it brings Link on to its back. From there, just slash away with the Sword, repeatedly hitting its eye. After a few hits, Link will be tossed away from Morpheel's back.
Repeat the same process once again, chasing Morpheel around the room. Since Morpheel swims rather quickly, it is difficult to chase after the eye, so try to intersect its path from other angles, sometimes even going head on in front of its mouth. Just be sure to claw on to its eye before it has a chance to suck Link in.
The only attack Morpheel has at this stage of the battle is swallowing Link, so try not to get sucked in. After latching on three times and swinging at its eye, Morpheel will be defeated.
In the first phase, use the Iron Boots and Clawshot to pull the eye away from its tentacles. Slash at its eye repeatedly until it retreats back. Repeat this process until Morpheel comes out from under the ground. Target the eye that is on top of Morpheel's head. Use the Clawshot to pull Link over and then slash away with the Sword. Repeat this process several times until Morpheel is defeated.