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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.

Summary:
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.