Forgive me if I'm wrong, I haven't gotten to this room yet, but can you just
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×kill the slayer against one of the corners? The room looks like you could exploit the technique that the entrance of this hold teaches:
http://forum.caravelgames.com/viewtopic.php?TopicID=11529
Namely, have him backed up against the corner with both your sword and his hook pointing diagonally out from the wall and towards each other. If you move towards him he'll defensively move back but the corners will force him to move diagonally exposing himself to attack. The hold linked above teaches the technique way better than I ever could. The entrance is essentially just a tutorial for this technique.
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Links to neat forum tools that I always have trouble finding:
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