If I'm to be honest, I kind of prefer the other version. In an effort to be "correct" to English grammar, you end up losing some of the character and gravity.
Japanese isn't afraid to drop subjects when they aren't absolutely necessary, so when Hacchi keeps addressing Machida by name straight to her face it ends up adding a very different gravity to the situation than him saying "you." If that gravity wasn't intended, he would have just been saying "I intend to win" (same sentence, but with the target of the "beat" removed) or used either "kimi" or "omae" instead of her name. It also goes against his character so far; he's getting more backbone, but he's not at the point where he'd be throwing out an open challenge where anyone present could misunderstand it as being directed at them, he'd be issuing the challenge and making it clear as day to everyone listening exactly who he is challenging. Addressing people by name to their face isn't that uncommon in English either, especially not when speaking directed statements in front of a group of people, and even more so when the person or people in question didn't seem to get the message the first time.