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