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