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