Arrghus protects itself with several eye monsters surrounded by a liquid substance and cannot be damaged until all the eyes are removed. To accomplish this Link must use the Hookshot to remove the eyes and make them vulnerable to attack, while Arrghus hovers slowly. He can also turn his eye monsters into flaming balls although they are fairly easy to avoid and one can attack and slay eye monsters even while Arrghus attempts this attack.
Once the eyes are removed Arrghus adapts a more aggressive tactic by attempting to pound Link into the ground with its body, this attack is easily avoided and one can land several hits before he attempts another pound. After 2-3 jumps Arrghus will fly away while trying to blast Link with several laser beams that explode on contact with the floor. While not overly difficult to avoid it can prove annoying if one runs directly after Arrghus while trying to evade the beams which can happen given Arrghus can move erratically while performing this attack. An easy way to avoid this attack is by using the Ice Rod which can successfully freeze Arrghus and stop the attack altogether, returning him to his pound attack. Rinse and repeat and Arrghus should fall with relative ease.
The name 'Arrghus' most likely comes from the Greek creature named Argus, which had eyes all over its body.