Can step on a fish quickly with his weighted boots
Large hands to grab more marine life
Rough gloves for traction on his victim so they can't escape
Diving helmet protects his head
Looks terrifying, making his targets easier to spot because they're running away
Light within the "eye" allows for enhanced vision
Role in movie
The Cyclops' existence is first heard of in the beginning of the movie when Mindy mentions him while she is warning SpongeBob and Patrick about the hazards of venturing out to Shell City, where King Neptune's crown is being withheld. The Cyclops is said to guard Shell City and is described as a giant when Mindy classifies him as the worst of the hazards.
Later in the movie, just when Dennis is about to step on SpongeBob and Patrick, the Cyclops finally appears, more specifically, his "bigger boot" (as SpongeBob and Patrick refer to it as) that accidentally and easily steps on Dennis, crushing him under the weight of the Cyclops, saving the duo from Dennis (at the moment), but unfortunately not necessarily from the Cyclops himself. Patrick is just about to make a run for it when SpongeBob notifies him that the hardhat diver's benefactor of a boot had saved their lives.
They display gratitude towards the pernicious diver for saving them from Dennis, referring to the Cyclops originally as "Stranger" for not knowing the Cyclops' true identity at the time, but the Cyclops just stands there, looking for his next victims. Then fear and realization strikes SpongeBob and Patrick when the Cyclops looks directly down at them, his hands ready to grab the two. SpongeBob and Patrick then discover that this abnormally large "stranger" who saved them from the evil Dennis was the even more monstrous Cyclops guarding Shell City, as mentioned in Princess Mindy's warning.
SpongeBob and Patrick try to run away, but with the diver's bigger boots clomping down behind them, fail miserably, and the Cyclops snatch them up tightly, gives them a long, menacing stare, and proceeds onward to the atrocious gift shop, Shell City, abducting the protagonists to the surface. SpongeBob and Patrick are stuffed in a bag and driven to Shell City in the Cyclops' boat (as shown in the script).
The Cyclops then puts SpongeBob and Patrick in his glass bowl and holds them captive in Shell City. First, he decides to scare them for entertainment, so he sneaks up behind them, stalks them a bit, exaggerates his breathing, and when SpongeBob and Patrick turn around, he scares the two and evilly laughs. He then gets over it, takes out a small toolbox SpongeBob refers to as his "evil instruments of torture." He then takes glue and googly eyes out and answers SpongeBob's question about what his business is with them by making a humorous diorama of "Alexander Clam Bell" out of a dead clam, a play hat, a small rotary phone, and the craft tools he took out of his toolbox while merrily humming to show them what he does to sea creatures and that they were next to be transformed into knick-knacks.
Once he had done these two things, he grabs SpongeBob and Patrick and places them under his heat lamp so they would dry up and die, giving him an opportunity to transform them into smelly knick-knacks. The Cyclops then grabs a book and goes into Shell City's restroom, also humming on the way there. Before their death, they both shed a single tear, which later rolls down the heat lamp's wire and shorts out a power outlet that smokes up, causing the fire sprinklers to set off. Apparently, they are in the bathroom too because as the two proceeded to lift Neptune's crown, one cam see the Cyclops picking it up and giving SpongeBob and Patrick a growl before the sea creatures the Cyclops had killed are revived.
One of the crabs squirts him in the face with his own glue and he ends up being swarmed by the other sea creatures, who proceed to beat him up for his actions on them.
Role in video game
His role in the video game is identical to his role in the film. The only level he appears in is "Google-eyes and Smelly Knickknacks." Where SpongeBob and Patrick are in Shell City, using King Neptune's crown to slide on a bunch of different colored hoses and electrical cables while trying to find a way out as the Cyclops pops up out of nowhere as they are sliding, and his hand appears out of nowhere in front of the jumps between the electrical cables on the higher level.