Ajax completely ignored the hat which had come from nowhere and been promptly swatted away by Ganondorf. He couldn't bring himself to care at the moment. He might tear it apart if he saw it again in a similar situation, but at the moment he was just beyond caring about it. The fight was over, he wasn't the one. Ajax shook his head. "You are strong, but that thing in your hand is what lets you fight me, and taking that shortcut means you cannot beat me". As Ganondorf charged for his final, almost certainly futile attempt at triumph, Ajax envied him somewhat. He missed that feeling, that glorious defiance in the face of defeat, that desperate attempt to overcome the odds and attain glory.
He could disable his adversary in a simple, effortless manner now. He could spend the bare minimum energy needed to subdue him, humiliate him and crush his spirit like that. But Ajax wasn't that kind of man. As Ganondorf charged towards him he stood still, measuring the distance between them and their respective reach. He was going to respond in kind. When the time was right, he pushed off his back foot and twisted his hips to add more power to his punch, launching a brutal right straight aimed directly at the tyrant's own fist, which seemed to hold the very source of his powers. He did not scream out, the time for words was past. All that was left was the end.