Like I said, I see it differently, I think it would be relatively easy for Harry to learn spells to deal with Anakin, and he might even know some already if he knew what Anakin can do. I don't really see what Anakin could learn that vastly improves his chances.
Do you think that Anakin's shortcoming is a lack of quick killing power? Because I don't, I think he can kill Harry fast enough in multiple ways, the only obstacle he could have is a spell that makes it impossible for him to dodge and get to Harry.