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