Here is the full list of all 55 Naruto Shippuden: Ultimate Ninja Storm 3 Full Burst trophies - there are 46 bronze, 6 silver, 2 gold and 1 platinum.
You won all trophies.
Got S rank in all boss battles.
Got S rank in The Last Battle.
Successfully performed all Secret Actions.
Completed the Ninja World Timeline.
Your total play time in Ultimate Adventure is over 30 hours.
Visited all villages.
Got S rank in Brothers, United.
Got A rank or higher in Brothers, United.
Saw all Secret Factors.
You cleared the fragments.
You cleared the last chapter.
Got A rank or higher in The Last Battle.
Got A rank or higher in Bet the Future.
Got S rank in Bet the Future.
You cleared Chapter 9.
You cleared Chapter 8.
Got S rank in The Rumbling Coast.
Got A rank or higher in The Rumbling Coast.
Got S rank in Threat of the Seven Swordsmen.
Got A rank or higher in Threat of the Seven Swordsmen.
Completed all Mission Battles.
You cleared Chapter 7.
You cleared Chapter 6.
Unlocked four or more Secret Factors.
You cleared Chapter 5.
You cleared Chapter 4.
Got four S ranks in boss battles.
Got A rank or higher in Overcoming Hatred.
Got S rank in Overcoming Hatred.
You cleared Chapter 3.
You cleared Chapter 2.
Got S rank in Hero and Avenger.
Got A rank or higher in Hero and Avenger.
Completed 50 or more Mission Battles.
Collected 10 or more Image Pieces.
The Tool Shop added to its ninja tool lineup.
Performed a Ring-Out KO.
You won the battle with a full health bar.
Performed a 50-hit combo.
Got A rank or higher in The Agitated Five Kage Summit.
Got S rank in The Agitated Five Kage Summit.
You cleared Chapter 1.
Triggered Burst Attack in a mob battle.
Used rear attack feature in a mob battle.
Used a coupon.
Finished a match with Team Ultimate Jutsu.
You cleared the prologue.
Got a ★x 5 Ninja Info Card.
Got A rank or higher in The Nine Tails' Attack.
Got S rank in The Nine Tails' Attack.
Unlocked a Secret Factor.
You won your first tournament.
Performed an Ultimate Jutsu Finish.
Successfully performed a Secret Action.