Here is the full list of all 38 Superdimension Neptune VS Sega Hard Girls (JP) trophies - there are 22 bronze, 11 silver, 4 gold and 1 platinum.
Acquired all trophies.
You caught all the balls.
You cleared the dungeon challenge.
You beat Delphinus.
All your characters maxed out their Lily ranks.
All your characters reached 99.
You reached level 99.
You unleashed Fever mode a 100 times.
You watched the bad Ending.
You watched the normal Ending.
You watched the true Ending.
You fought 500 battles !
You cleared a 100 different missions.
Your investigation skills reached level 25.
You earned a million credit.
You chatted with all the Hard Girls.
DREAMCAST joined your party.
UZUME joined your party.
Toyporisu Third floor unlocked.
Toyporisu Second floor unlocked.
You maxed out your Lily rank.
You inflicted over a 100 Hits.
MEGA DRIVE joined your party.
PURURUT joined your party.
You inflicted over 100,000 damage points to an enemy.
GAME GEAR joined your party.
NEPGEAR joined your party.
SEGA SATURN joined your party.
NEPTUNE joined your party.
You fought a 100 battles !
You challenged History Destroyer.
Toyporisu has been unlocked.
You changed Class.
Fever mode unleashed.
You caught a ball.
First fight cleared.
You took your first time leap.
Started the game.