Successfully complete one of the following tasks to get a trophy:

In Title Only (Bronze): Make sure to check your titles. You can acquire titles at the Adventurer's Guild in town.
The More The Merrier (Bronze): Execute a coordinated attack with six characters.
Alchemical Aptitude (Bronze): You have added an item to the shop. Keep doing alchemy to add more.
Can We Keep Him? (Bronze): Captured a monster.
I've Created a Monster! (Bronze): Combined monsters.
We Can Rebuild Them (Bronze): Created three marionettes.
Special Delivery (Bronze): Used your first Special Art
Well-Read (Bronze): Every profile is not available.
I've Seen Everything (Bronze): Every item in the gallery is now available.
The First (Silver): Cleared Generation 1.
The Second (Silver): Cleared Generation 2.
The Third (Silver): Cleared Generation 3.
The Fourth (Silver): Cleared Generation 4.
The Fifth (Silver): Cleared Generation 5.
For Real This Time (Gold): Saw the true ending.
Titular (Gold): Earned every title.
Consummate Consummator (Platinum): Earned every trophy.

Additionally, there are 18 secret trophies:

Secret trophy (Unknown): Unknown.
Secret trophy (Unknown): Unknown.
Secret trophy (Unknown): Unknown.
Secret trophy (Unknown): Unknown.
Secret trophy (Unknown): Unknown.
Secret trophy (Unknown): Unknown.
Secret trophy (Unknown): Unknown.
Secret trophy (Unknown): Unknown.
Secret trophy (Unknown): Unknown.
Secret trophy (Unknown): Unknown.
Secret trophy (Unknown): Unknown.
Secret trophy (Unknown): Unknown.
Secret trophy (Unknown): Unknown.
Secret trophy (Unknown): Unknown.
Secret trophy (Unknown): Unknown.
Secret trophy (Unknown): Unknown.
Secret trophy (Unknown): Unknown.
Secret trophy (Unknown): Unknown.