After the scene, run across the bridge as it collapses. Just jump and follow the QTE actions prompted on your screen to finish this sequence. Once you caught up with Castor, throw a stone at him to start the boss battle.
For the first phase of the battle, you just have to time your evasion against Castor's basic three-hit combo. Continue dealing damage to him until he gives off health and magic orbs. He will then smash the ground, making it crumble beneath your feet. Round around from left, down then right to avoid falling in the abyss below.
In the next phase, Castor will begin deploying movement-restricting auras in the battlefield and he'll also deal considerable AOE (area-of-effect) damage upon impact of his attacks, as well as the ability to release a mid-range shockwave. He'll be vulnerable right after his impact smash so use that time to attack then quickly evade as soon as he recovers. Keep doing this until he charges up again and destroys all the pillars in the area. Grapple the boulders from the pillars and haul them over to Castor to deal damage and recover a bit of your HP if the throw connects.
After this, Castor will start attacking from above the pillars. The pillars will turn gray, indicating that you can smash it to pieces. Castor will shoot you with projectiles in this phase and will also make the floor crumble. You can continue destroying the pillars until you can catch up with him and destroy the pillar he's on or use the boulders from the pillars you destroyed earlier. Either way, this will make him fall to the ground and stagger him. Use this chance to deal massive damage.
Once he recovers, he will begin a series of lightning-fast slashes. You can block these but be prepared to evade either an aerial smash or grapple follow up. He'll be open after his series of slashes or the air smash so be ready to counterattack when you have the chance. He'll also occasionally deploy his movement-restricting auras and shockwaves so be careful of those as well. Keep dealing damage until he flies in the air and starts destroying the floor again.
Strike where it hurts most
For the last sequence, you have to correctly press the QTE buttons to finish Castor off.
Finishing off an impudent abomination