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