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