I'm almost done with the game, and it's definately an 8 in terms of the usual mainstream reviews (Gamespot, IGN, etc).
Cutscenes: It's got some of the best cutscenes in an action adventure game. The voice acting is great, fits the mood of the game just right.
Visuals:Not perfect, but still amazing. There are some awesome locales, and I love just taking in the beauty of it all.
Battle: I'm not a hardcore fan when it comes to battle systems, as I have barely any experience with Ninja Gaiden, but comparing the two, it definately doesn't feel as fluid. The attacks are fun to pull off, its nice to know a couple of the block breakers and multi hit combos, and its definately rewarding to see the grace of her attacks.
Bosses: I liked the boss fights, but they aren't as epic as they could be.
Framerate: Gets a choppy, doesn't ruin the game, but still noticable.
Kai / Shooting sections: Like everyone mentioned, a fun diversion from the main action. Actually one of the first sidekick kind of things I actually enjoyed. I love the use of the sixaxis is this regard.
"Puzzles": The weakest part of the game and the most frustrating. Throwing hats at gongs is silly, and just annoys me everytime I do it. Feels like just another excuse to do something with the Sixaxis, which is a shame considering I liked the use of it in everything else. Please get rid of this.
Level Design: I don't know if the linear feel of the levels is good or not, I feel a little indifferent about it. Would it be better with more complex level design? Not sure.
Anyways, the game is what I want out of any game. It gives a great experience, and you'll have fun, theres no denying that.