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