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