The battle starts with Byrne jumping along pillars and occasionally shooting weak beams towards Link, which can be easily dodged. Eventually Byrne will attempt to hit Link with his massive gauntlet arm. If Link dodges out of the way the gauntlet arm will get stuck in the ground. The phantom can then run over to the gauntlet and she will pull on it, causing Byrne to fall to the ground. Link can then run on over and get a few sword slashes in before Byrne gets back up. After repeating this process a few times Byrne will stay on ground level.
At this point Link can run up to Byrne and slash at him repeatedly. He will block the first two attacks but the third one will usually hit. After Byrne is a bit shaken up, he will now perform a large purple charged attack towards Link. When he is charging up, Link can go hide behind the phantom. When Byrne charges in, the phantom will grab Byrne and hold him steady. Link can once again run over and deliver some sword slashes while Byrne is stuck.
Afterwards, Byrne will get a bit quicker with his attacks and does a better job of blocking Link's sword attacks. After a few more repetitions of the process Byrne will be defeated without much of a sweat.