For this trophy you'll need to earn an S Ranks across ALL Boss Battles in the Story.
For FACTORS on reaching high Rank for Boss/Pseudo battles please consult with this trophy solution:
There are a total of 8/9 Boss Battles that require an S Rank for this achievement. These battles are as follows:
-Nine Tails' Attack: Third Hokage vs Nine-Tails, Minato vs -Masked Man.
-The Agitated Five Kage Summit: Sasuke vs Gaara, Sasuke vs Samurai, Sasuke vs Mizukage
-Hero and Avenger- Naruto vs Sasuke
-Overcoming Hatred: Naruto vs Nine-Tails* earliest
-Threat of the Seven Swordsman: Guy, Sakura, Lee, vs 6 Swordsman, Kakashi vs Zabuza
-The Rumbling Coast: Choji vs Gedo Statue
-Bet the Future: 5 Kages vs Madara Uchiha
-The Last Battle: Naruto vs Jinchuriki & Tobi
NOTE: IF YOU HAVE THE FULL BURST DLC, OR RETAIL VERSION, YOU WILL NEED TO BEAT SAGE MODE KABUTO, WITH THE S RANK, IN ORDER TO GET THIS TROPHY.
If, for any reason, you aren't able to earn an S Rank no worry. You can retry ANY battles post-story in the Ninja World timeline for another try.