This is possibly the most difficult and aggravating fight of the entire game. Firstly, pull out a quicktime button sequence guide (Unknowable Moment achievement guide). This will save you some stars, and thus increase your rank.
Fighting Kakuzu is a painful encounter. Dispose of his first form easily using jutsu and substitutions. Then he awakens into some freaky form. Continue to fight him off until a cutscene comes through and he gets enormous.
This is where it gets fun (not). He will begin to shoot things at you.
-Air Currents. These will come out in triplets. Simply stay out of the path and they will not hit you, you can sometimes stay still.
-Fireballs. Start from one end of the stage. Just push your analog stick the opposite direction. Your run is faster than his shot. You should be fine. Do NOT jump.
-Tail whip. Simply run away, it usually doesn't hit. If he tries to slide it, either keep running or jump over it. I prefer to run.
-Underground spikes. Same as fireballs.
-Fire and Air Beam. Here's where it gets weird. He will pause a moment before initiating this, so don't start running immediately. But you do want to run... After the beam is through, run up to Kakuzu and press "B". Then a mashing segment will commence and you'll rip him out. Beat the crap out of him until he "awakens". He will back up, and all of the above will begin to rain down upon you. Do your best to evade, and even use a Rasengan to push through if you need to. Get close, and let Kakuzu have it, but don't push him too close to the structure or else he'll go back in early.
Rinse and repeat until the achievement pops.