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