Pollux & Castor are a boss that Kratos encounters in Chapter 12 - The Oracle's Chamber. The following is a strategy to use against them in the fight.
Castor is quick and quite deadly with his attacks. When the battle begins, grapple the nearby rock to toss it at him, which will make him repair the arena and begin the first phase of the battle. During this phase, he will begin by destroying the center of the arena before repairing it again. He employs a lot of close range attacks, trying to hit you with his weapon, as well as sending out a shockwave straight ahead. He's usually vulnerable to a single combo in between his own combos.
Whenever you see orbs come out from him, he will float into the air and start destroying the arena, piece by piece. Stay on the right side and when you see the central pieces come back, jump to them. It's time for the second phase, where he will be teleporting around a lot. He lays circles down on the ground at times, which slow you down considerably if you're inside them.
Besides that attack, he reuses some of the same attacks as last phase. He does have a ground pound with shockwave, which is usually preceded by him floating in the air for a second or two. Whenever he knocks down the pillars, there will be rocks laying around, so grapple them to toss them at Castor, which results in a health and magic orb for you.
Eventually, he'll restore the pillars and start teleporting around the tops of them. While on them, he will shoot some projectiles at you and pieces of the arena will crumble away. Here, you want to go to each of the pillars and hit them until they break. Once the fourth is down, he will be vulnerable for a few seconds before moving to the next phase.
This next phase might be the hardest, simply because it's difficult to dodge all of his attacks. He likes to teleport close to you and slash you with his weapons multiple times, with his finishing move being the ground pound shockwave from before. He will also try to teleport close to you and attempt to grab you, so make sure you're always rolling away.
You know you're doing everything right when you teleports to the north end of the arena and destroys most of it, surrounding himself in a green sphere. When he does this, move to the far southcentral part. You'll go into a first-person view and Castor will teleport around, eventually landing in front of you. Hit the buttons that appear, then hit Square to knock him away. Grapple him and then keep pressing Square to beat him up some.
It's now time for Pollux to take over. He will do nothing but fire projectiles at first, which can be blocked, but he will also try to melee you at times. He will also destroy the north and south portions of the arena, floating up in the air and firing more projectiles. Eventually, he'll surround himself with the slow-down circle, making it slightly difficult to get good hits on him.
Once you've damage him enough, he'll go into the middle of the arena and destroy the platform to the north with the Oracle. He'll start destroying the arena as well, but you can stop him by going up and hitting him until he stops. Now it's your chance to grapple him and do the final QTEs to finish him off for good.
