Here is the full list of all 50 Naruto: Ultimate Ninja Storm trophies - there are 37 bronze, 11 silver, 1 gold and 1 platinum.
Acquired all the trophies.
Won a Jutsu Clash.
Finished an opponent with an additional strike after downing them.
Acquired over 50% of all Ultimate Jutsu Movies.
Acquired over 30% of all Ultimate Jutsu Movies.
Acquired an Ultimate Jutsu Movie.
Acquired over 50% of all music files.
Acquired over 30% of all music files.
Acquired a music file.
Acquired over 50% of all Figures.
Acquired over 30% of all Figures.
Acquired a Figure.
Completed over 50% of the missions.
Completed over 40% of the missions.
Cleared 42 or more rings with one Naruto Cannon.
Cleared 24 or more rings with one Naruto Cannon.
Six or more different items were added to the shop.
Completed the Chasing Sasuke Arc.
Finished an opponent while Awakened.
Completed over 30% of the missions.
Destroyed 10 or more objects with one shuriken toss.
Destroyed five or more objects with one shuriken toss.
A new item was added to the shop.
Completed the Tsunade Search Arc.
Destroyed a door with a Rasengan.
Cleared 12 or more rings with one Naruto Cannon.
Completed the Leaf Destruction Arc.
Completed over 20% of the missions.
Finished an opponent with a Support Combo.
Acquired 14 or more Ninja Handbooks.
Finished an opponent with an Ultimate Impact.
Finished an opponent with a throw.
Completed the Chunin Exam Arc.
Acquired eight or more Support Ninjutsu Books.
Finished an opponent with an Ultimate Jutsu with the Storm Gauge at MAX.
Prevented an opponent's Extra Hit.
Completed over 10% of the missions.
Created 10 or more different Ichiraku Ramens.
Finished off an opponent from a wall.
Created a new Ichiraku Ramen.
Acquired a Support Ninjutsu Book.
Performed six or more successful rope actions.
Acquired a Ninja Handbook.
Completed the Genin Training Arc.
Interrupted an opponent's Ultimate Jutsu.
Finished an opponent with Support Ninjutsu.
Finished an opponent with Ninjutsu.
Attacked an opponent with a Supportive Extra Hit.
Finished an opponent with an item.
Finished an opponent with an Ultimate Jutsu.