Michael Felix wasn't a fool, and knew that he stood no chance against the Third Prince. He wasn't trying to beat him, just be seen as capable by him and General Skye. They were the strongest and most respected officers in the entire military, and he wanted to be on their radar in a good way..
Shasta had taken an interest in him due to his skill as a Manic, and had told him stories about both Tidas and Skye while they were away. He had already admired Tidas for years from the corner of the banquet hall, but Princess Skye's story was new and astonishing to him.
All Michael had known about Skye were her skills as a Shaman, her unusual generosity, and that she was incredibly powerful. He had watched her victory in the Mage Trials the previous year, so he knew that she had four traits. Skye was just an overly gifted noble to him, but he learned from Shasta the truth of her father's elevation in status.