At first, it appears to be an anemone- or Charybdis-like creature with a single eye that constantly moves through the tentacles and must be extracted via Clawshot. After some time it shoots out Bombfish which Link has to throw at it and take them with his Clawshot to defuse them. After taking enough damage, Morpheel erupts out of the ground, revealing that it is an enormous, lamprey-like creature, and that the tentacles are only its feelers.
The manner of which Morpheel is fought in its first form is identical to that of Morpha from Ocarina of Time. Morpheel's tentacles resemble Morpha's ability to extend a tentacle-like water funnel from its watery body. Morpheel can also move its single eye through its many tentacles, in the same way Morpha can move its nucleus throughout the funnel of water, and both have to be removed with their represented game's hook device. Morpheel's American name is a combination of "morph" and "eel", and shares the same prefix, "morph", with Morpha, which it is named after. Its Japanese name is simply a reference to the fact that it has eight feelers.
When Link enters Morpheel's chamber, the young hero only finds a single tentacle at the bottom. Once Link sinks to the sand, several other tentacles emerge from the bottom of the chamber and the fight begins.
Morpheel's first form is simple to defeat. Link must equip the Iron Boots, avoid the Bombfish it releases, then grabs its eye with the Clawshot. The young hero must then attack it immediately and repeat the operation. After two times, the creature's tentacles retract, and its eye gets swallowed, ending up on his back. Link must proceed to swim above it in order to use the Clawshot to latch onto the eye, the Critical Point. After slashing away, Link is thrown off. The young hero must continue to do this a few more times for the monster to go down. Once it has sustained enough damage, Morpheel will finally crash into the wall, draining all the water in the room.
Given the fact that the previous two bosses (Diababa and Fyrus) were normal beings mutated by the Fused Shadow (a Deku Baba and Darbus, respectively), it would be logical to assume that Morpheel was also once a normal creature, most likely a Bombfish given its physical resemblance to and capability of birthing them. It could also possibly be a Skullfish, given that there are many of them swimming in the waters around the column in which it resides, or perhaps even a Hyrule Loach, given the presence of those fish throughout the Lakebed Temple.
The strategy for defeating Morpheel incorporates the strategies for defeating both Morpha and Molgera.
The chamber where Morpheel is fought is possibly one of the largest chambers in the Zelda series.
When Link first enters, if he swims around the surface of the chamber, Midna will suggest that he dives.
Link grabbing Morpheel's eye with the Clawshot
Link slicing Morpheel's Critical Point
Morpheel's eye turning into a Heart Container
Link fighting Morpheel
↑ "Looks like that eyeball is pretty important to him... See if you can't [L]-target it and yank it right out of the tentacle!" — Midna (Twilight Princess)