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.
You challenged History Destroyer.
Toyporisu has been unlocked.
You fought a 100 battles !
You changed Class.
Fever mode unleashed.
You caught a ball.
First fight cleared.
You took your first time leap.
Started the game.
Acquired all trophies.
NEPTUNE joined your party.
NEPGEAR joined your party.
PURURUT joined your party.
UZUME joined your party.
MEGA DRIVE joined your party.
GAME GEAR joined your party.
SEGA SATURN joined your party.
DREAMCAST joined your party.
You watched the normal Ending.
You watched the bad Ending.
You watched the true Ending.
You beat Delphinus.
You fought 500 battles !
You inflicted over a 100 Hits.
You inflicted over 100,000 damage points to an enemy.
You unleashed Fever mode a 100 times.
You earned a million credit.
You cleared the dungeon challenge.
You cleared a 100 different missions.
Your investigation skills reached level 25.
You caught all the balls.
Toyporisu Second floor unlocked.
Toyporisu Third floor unlocked.
You chatted with all the Hard Girls.
You reached level 99.
All your characters reached 99.
You maxed out your Lily rank.
All your characters maxed out their Lily ranks.