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