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