By "beat" I meant making him give up.
You can make him give up by winning over and over again in your first phase.
But your second phase is unironically weaker than your first phase (atleast from gameplay perspective), which makes it nearly impossible to defeat him enough times to make him give up in the "final fight" where dialogue says "Lets see your corpse burn one last time".
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I don't know if this is relevant, but even if I was always going into the second phase because of beng bad at the game (it was my third run), I was actually able to kill the hero in that "final fight", but it lead to him coming back and having another dialogue, althought I couldn't see if there was an ending since the game glitched due to me killing him in the first phase with the normal melee attack at the same time he hit me with his sword, triggering the second phase while he was dead. I got stuck in the second phase, my hp bar was not showing, neither was the hero's, and the hero was stuck in a running animation loop, following the queen at her left, right under her. I then spammed the second attack, but the hero was ivulnerable, probably due to the glitch, and I died somehow, triggering the normal ending. I reached there when I was only using the first options in the dialogues.
Also, I'm unsure about this, but I think in my first playthrough, the one I got the ending where you say that you don't want to hurt the hero (I later died to doing nothing when I chose that dialogue option). Is there a different ending with it? I don't know if it is my memory being bad, but I think in that plathrough the queen never kneeled and just touched him to burn him to ashes, she skipped that and hugged him, before I even reached the second phase. Also, when I reached the second phase, I think that the torches were unlit instead of being purple, although I'm not sure about this one.