Here is the full list of all 42 Persona 3: Dancing in Moonlight trophies - there are 26 bronze, 12 silver, 3 gold and 1 platinum.
Obtained all trophies.
Watched all Social events.
Obtained all of the accessories.
Obtained all rewards from Elle-P's card search.
Obtained all the costumes.
Unlocked all Custom modifiers.
Obtained all the pairs of glasses.
Explored all the guys' rooms.
Watched every possible dance for Aigis.
Watched every possible dance for the P3 Protagonist (Makoto Yuki).
Started a stage on ALL NIGHT difficulty with 10 or more Challenge modifiers enabled.
Had Elle-P join the ball.
Made Elle-P's ball a success.
Cleared a stage with 5 Challenge and 5 Support modifiers simultaneously enabled.
Cleared a stage with both "Note paths waver" and "Note speed fluctuates" enabled.
Cleared a stage after changing Hype Gauge difficulty in Custom.
Unlocked all ???s in Collection.
Cleared the stages where Fuuka and Ken dance together.
Cleared a stage on HARD or harder with all Support modifiers enabled.
Cleared the stages where Yukari and Junpei dance together.
Cleared the stages where Akihiko and Mitsuru dance together.
Watched 40 different Fever Time dances.
Obtained 5 rewards from Elle-P's card search.
Explored all the girls' rooms.
Obtained half of all the accessories.
Started a stage with a different hairstyle, two accessories, colored contacts, and a colored wig.
Cleared a stage with both "GOOD ratings won't break combos" and "Game Over with combo break" enabled.
Explored a friend's room.
Cleared a stage on HARD or harder and earned a PERFECT rating on at least half of the Notes.
Earned the highest possible grade on a stage (KING CRAZY).
Unlocked the highest difficulty level (ALL NIGHT).
Obtained half of all the costumes.
Registered a costume as a Favorite.
Watched 20 Social events.
Changed costumes and played a stage with each of the members of SEES (excluding Koromaru and Shinjiro).
Failed a stage.
Watched a replay.
Beat your own high score.
Cleared a stage.
Watched a Social event.
Played a tutorial.
Obtained a costume.