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