Here is the full list of all 38 Superdimension Neptune VS Sega Hard Girls trophies - there are 22 bronze, 11 silver, 4 gold and 1 platinum.
Acquired all trophies.
You cleared the dungeon challenge.
You caught all the balls.
All your characters maxed out their Lily ranks.
All your characters reached 99.
You reached level 99.
You beat Delphinus.
You saw the Normal Ending.
You saw the Bad Ending.
You saw the True Ending.
You cleared a 100 different missions.
Your investigation skills reached level 25.
You chatted with all the Sega Hard Girls.
GAME GEAR joined your party.
NEPGEAR joined your party.
DREAMCAST joined your party.
UZUME joined your party.
You earned a million credits. Wow.
You fought 500 battles !
You activated Fever Time 100 times.
SEGA SATURN joined your party.
NEPTUNE joined your party.
You dished out over 100 Hits.
Toypolis Third Floor unlocked.
Toypolis Second Floor unlocked.
You performed a Class Change.
MEGA DRIVE joined your party.
PLUTIA joined your party.
You inflicted over 100,000 damage points to an enemy.
You maxed out your Lily rank.
You challenged the Time Eater!
Toypolis been unlocked.
You fought 100 battles !
Fever Time activated.
You caught a ball.
You finished your first fight! Aw.
You made your first leap through time.
Fired up the game!