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He will pull out two swords and start attacking. He will either spin for a long time or flail his swords around. You cannot hurt him until after he is done spinning, where he will be dazed for a few seconds. You can also defend repeatedly with your shield.
Zant will be in front of Hyrule Castle. If he is spinning, run. If he is flailing, however, you can either charge him or do a backslash to hurt him. After a long while, he is finally defeated.