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