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