Here is the full list of all 51 3D Dot Game Heroes (EU) trophies - there are 42 bronze, 5 silver, 3 gold and 1 platinum.
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Cleared Spelunker mode.
Survived Spelunker mode for 10 hours.
Cleared the game in FROM mode.
Cleared the game without restoring the princess.
Cleared the Spelunker event.
Acquired all the swords.
Booked all monsters in the Bestiary.
Booked Onyx in the Bestiary.
Booked Fuelle in the Bestiary.
Cleared the game without dying.
Cleared the game with the princess restored.
Defeated Onyx without taking damage.
Defeated Fuelle without taking damage.
Visited all maps.
Booked Dragon in the Bestiary.
Booked Dark Knight in the Bestiary.
Booked Kraken in the Bestiary.
Booked Queen Bee in the Bestiary.
Booked Eelagon in the Bestiary.
Booked Giga Golem in the Bestiary.
Maxed out the Giga Sword.
Collected 777G.
Maxed out the LIFE bar.
Acquired the Hero Shield.
Maxed out the MAGIC bar.
Spent the night in Raejack with the princess.
The princess was restored to her true form.
You found Ai.
Defeated Dark Knight without taking damage.
Acquired the Hero Sword.
You found Sue.
Defeated Dragon without taking damage.
Defeated Kraken without taking damage.
Defeated Queen Bee without taking damage.
Defeated Giga Golem without taking damage.
Booked a monster in the Bestiary.
Defeated a foe with a bomb.
Defeated a foe with a bow.
Acquired a sword from King Block.
Acquired the Holy Sword.
Made your sword stronger at the blacksmith.
Played the game for five hours.
Used a Shader Magic.
Took a snapshot.
Defeated Eelagon without taking damage.
Guarded an attack.
Acquired the Ancient Sword.
Defeated a Guardian.
Defeated a foe with a sword.
Made a character model.