Spanda's favorite squid
On the first phase, Arrghus will have smaller "puffs" surrounding it. Each puff has 8 HP. It will have any remaining puffs orbit around the boss arena in an attempt to damage Link.
On the second phase, the main eye of Arrghus will be open to attacks. It will spring into the air and crashes onto the ground.
On the second phase of the fight, pause the game and switch to the Fire Rod. Fire it in the bottom of the room, nearby the shutters as soon as Arrghus lands. With enough practice, you can easily zero-cycle it.