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