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