The Beast will usually only attack with slashes and biting, doing moderate damage to Sora, similar to his basic fighting style in Kingdom Hearts. However, Beast can also use a powerful roar attack, and will occasionally send Cogsworth out of commission by telling him to "Leave, NOW!!!", but this is only a temporary effect.
Nearly all of the duration of the fight, the Reaction Command "Wake Up" will be usable. It does more damage than attacking with the Keyblade; however, it is faster to fight him regularly. The Reaction Command does stun the Beast for a short period, so Sora can attack him without fear of reprisal.
Continue to fight Beast until his health bar is empty. When it is, he will bend down on one knee. The Reaction Command "Charge" will show up. Tap rapidly, and the Beast will come to his senses.