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