So this volume is mostly a training montage. As with the first volume, if you've already seen the movie, you won't be getting anything new out of this. Except maybe an image of luscious Kaede lips. I thought that was an odd panel, considering the tone of the rest of The Boy and the Beast.
In this volume, "Kyuta" grows up during the before-mentioned training montage. He finds his way back to Tokyo and meets the girl Kaede, who serves as teacher and cheerleader. Even in the movie, I felt like they wasted her potential as a character, and with the way the manga's following the movie so closely, I don't think they'll be doing much more with her.
This volume improved on the "action" scenes, so I guess that's something.
All in all, I think I'll stick with my opinion from my review of the first volume: you might as well just watch the movie.