The Red Bull is the story's secondary antagonist. It's not actually a bull, but a fiery elemental fae creature in the shape akin to one. He is the most powerful servant to King Haggard, boasting incredible power, control over fire, the ability to grow in size from the size of a large bull to bigger than an elephant, and the ability to rapidly travel as a ball of fire. The bull might seem like a mindless monster, but it is heavily implied it's actually sapient and just doesn't speak. While baffled at Amathea's transformation into a human, it clearly knows something isn't right and patrols the region trying to figure out what happened to the last unicorn. Upon seeing her again, even if she had looked and acted more human than ever, it instantly figures out who she is.
The exact nature of the bull is left vague. Several possibilities are brought up including that Haggard is the bull via some kind of astral projection, that the bull is a captive by Haggard and forced to work, or that the bull's territory is around Haggard's castle and he's imprisoned by the monster. While never directly clarified, it does appear the bull is an independent entity as it continued to function independent of Haggard. Under the latter's instructions, the Red Bull had drove the unicorns of the lands into the ocean to keep them imprisoned for Haggard's will, and covered up the remaining Unicorns' hoof marks by trampling them and keeping everyone away from the castle and cove the unicorns were imprisoned in.
After resuming it's chase of the unicorn in the finale, it stampeded and trampled Prince Lir when he got in the way, inspiring the unicorn to fight back. Stood up to by his quarry and with Haggard's influence waning, the bull relented and back down. Upon it walking off into the ocean to leave the heroes in peace, the captive unicorns were all set free.
It was based on a painting Peter S. Beagle found with Unicorns battling Bulls (one of them was Red).
The roars are similar to the Fell Beast on Return of the King (from the same creators). Both are taken from stock sound effects of the diakaiju Gamera.