Here is the full list of all 45 Kingdom Hearts: Melody of Memory trophies - there are 30 bronze, 11 silver, 3 gold and 1 platinum.
Get the moogle to the highest level.
Clear 50 songs on Standard.
Unlock all Story Archive movies.
Clear the game and view the ending.
Defeat 10,000 enemies.
Complete all missions in 10 worlds.
Play 100 Music Stages.
Defeat a COM opponent.
Clear all songs in 50 worlds.
Earn 2,000 EXP or more in one song.
Use every team at least once.
Achieve a total score of 500,000,000.
Clear 50 songs on Beginner.
Clear all songs in 30 worlds.
Clear a Boss Battle Music Stage.
Hit 100 friend orbs.
Clear all songs in 10 worlds.
Get a Full Chain.
Clear all songs in a world.
Obtain all trophies.
Clear 50 songs on Proud.
Clear 50 songs with a Full Chain on Beginner.
Clear 50 songs with a Full Chain on Standard.
Clear 50 songs with a Full Chain on Proud.
Defeat 50,000 enemies.
Defeat 100,000 enemies.
Achieve a total score of 2,000,000,000.
Collect 50,000 Rhythm Points.
Play the same Music Stage 10 times.
Use 100 items.
Find 100 treasure chests.
Obtain 10,000 items from Music Stages.
Synthesize 100 items.
Defeat 20 COM opponents.
Reach Platinum 1 rank in COM Battle.
Attack the same enemy 19 times or more throughout one song.
Spend one minute or more gliding in a Field Battle Music Stage.
Fight alongside King Mickey for an hour.
Clear all five of Today's Tunes with a Full Chain.
Reach the highest level with Team Classic.
Clear all songs in all worlds.
Clear all songs on Beginner.
Clear all songs on Standard.
Clear all songs on Proud.
Play all songs.