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