S ranks are primarily driven by how much health you have remaining and the number of stars you have from the quick time events at the end of the fight. Oddly enough, the more stars you get the more health you recover. That said, you'll naturally want all of the stars you can get. Quick time events occur when the character icon begins to flash, so be ready once you see this.
This trophy is rewarded for going against Kakuzu after Naruto finishes the training for his new jutsu. This is easily the most annoying of the boss fights, however if you play it conservatively you should be fine. The first form is nothing special, it is easily defeated using ninjutsu spam or even a chakra dash in to some melee strings. After he backs off, the first quick time event section begins.
The commands occur in this order...
O O X
X X O
X Triangle O
X X Triangle O
The second form is just like you would be fighting somebody in their awakened state. Ninjutsu spam is a safe bet, as the rasengan hurls you towards him however it really is based on how you want to do the fight.
After you do some damage, his icon will shine but it is not for the sake of a QTE but for yet another transformation. This one is the real pain, so I hope you saved a good portion of your life bar. He has a few attacks, he can fire some fireballs in your direction which come in waves of 4. He also can attack the ground and have tentacles rise from the ground, along with a shockwave that breaks in to three separate sections which move along the ground. It's key that you simply avoid these attacks and try to hang near one edge. The reason you should hang near the edge is he will charge himself up after you dodge for a few moments and fire a concentrated beam which reaches across the whole map. The only way you can avoid it is by running away as he's firing and being able to move along the map for a solid 3-4 seconds. After he does this, you can dash up to him and press O to rip him out and strike.
After you do your damage, he will have a red aura surrounding him and his attacks will blend together. Primarily focus on dodging at this part otherwise you'll take a good chunk of damage, especially considering he's immune to physical attacks. If you feel brave, I'd suggest pressing Triangle and then Square for some windmill shuriken.
The key thing here is trying not to lose too much life, which is no easy task. You'll get a good chunk of health back after this next quick time event, but you can't be too careful. After getting him low on his dark red health bar, you'll see his icon begin to flash. The commands are as follows.
Triangle X X
Up X X
Left Triangle Triangle O
Personally I only had 61% health at the end, after getting all of the stars. This one may give some leeway considering the fact it's a tricky boss battle. Best of luck, if you have done this one the rest will be cake!