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.
Finished an opponent with an additional strike after downing them.
Won a Jutsu Clash.
Acquired over 50% of all Ultimate Jutsu Movies.
Completed over 40% of the missions.
Acquired over 30% of all Ultimate Jutsu Movies.
Destroyed 10 or more objects with one shuriken toss.
Destroyed five or more objects with one shuriken toss.
Completed the Chasing Sasuke Arc.
Cleared 42 or more rings with one Naruto Cannon.
Cleared 24 or more rings with one Naruto Cannon.
Finished off an opponent from a wall.
Completed over 30% of the missions.
Interrupted an opponent's Ultimate Jutsu.
Cleared 12 or more rings with one Naruto Cannon.
Acquired an Ultimate Jutsu Movie.
Six or more different items were added to the shop.
Completed the Tsunade Search Arc.
Destroyed a door with a Rasengan.
Acquired over 50% of all music files.
Completed over 20% of the missions.
Acquired over 30% of all music files.
Finished an opponent with a Support Combo.
Completed the Leaf Destruction Arc.
Acquired 14 or more Ninja Handbooks.
Acquired a music file.
Acquired over 50% of all Figures.
Finished an opponent with an item.
A new item was added to the shop.
Acquired eight or more Support Ninjutsu Books.
Finished an opponent while Awakened.
Completed the Chunin Exam Arc.
Created 10 or more different Ichiraku Ramens.
Completed over 10% of the missions.
Acquired over 30% of all Figures.
Acquired a Figure.
Performed six or more successful rope actions.
Acquired a Support Ninjutsu Book.
Created a new Ichiraku Ramen.
Finished an opponent with a throw.
Prevented an opponent's Extra Hit.
Finished an opponent with an Ultimate Impact.
Acquired a Ninja Handbook.
Completed the Genin Training Arc.
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.
Finished an opponent with Support Ninjutsu.
Finished an opponent with an Ultimate Jutsu.