There are 46 Trophies that can be earned in this title.

Bronze

Neptune Start
New game started

Combo Making
Created an original combo

Item Making
Synthesized item used in battle

Shopping
Purchased items

News
Gathered information led you to find and clear a quest

Medieval Fantasy
Arrived in LEANBOX

Steam Punk
Arrived in LASTATION

Marchen
Arrived in LOWEE

Future Fantasy
Returned to PLANEPTUNE

Dress Up
Accessory changed

OVER CLOCK
Processor unit changed

Teamwork
Battle formation changed

Hard Battle
Fought in Patron godess form during battle

Nippon Ichi
Nippon Ichi joined your group

GUST
GUST joined your group

Silver

Scenario Completion
Scenarion cleared

Multi-Platform
Walked through the entire map

Gold

Speed Searcher
Completed all the time attack in S-Class

History Document Histoire
Obtined all histoire

26 Secret

http://www.ps3trophies.org/game/hyperdimension-neptune/trophies/