There are 47 Trophies that can be collected.

Bronze

Nepgear: Engage!    
Started up a new game in Gamindustri.     

Gamindustri Graveyard    
View a certain CG Image.     

CPUs, Bound and Gagged    
View a certain CG Image.     

HDD Force Start    
View a certain CG Image.     

Dogootastic!    
View a certain CG Image.     

The Big CPU Gig    
View a certain CG Image.     

Histoire's Nostalgia    
View a certain CG Image.     

CPUs, Unbound and Free    
View a certain CG Image.     

Obligatory Hot Spring Event    
View a certain CG Image.     

LAN Party!     
View a certain CG Image.    

C-C-C-Combo Attack    
Created your own combo.     

It Ain't Alchemy    
Developed an item.     

Lastation's CPU Candidate    
Met Uni.     

Lowee's CPU Candidates    
Met Rom and Ram.     

Nep-Nep's Back    
Neptune joined the party.     

Vert's Return    
Vert joined the party.     

Noire's Revenge    
Noire joined the party.     

Blanc's Vengeance    
Blanc joined the party.     

Gamindustri's Heroine    
Nisa joined the party.     

Gamindustri's Alchemist    
Gust joined the party.     

Gamindustri's Pop Idol    
5pb. joined the party.     

IF's Rehab Clinic    
Performed battle for the first time in years.     

Evil's Nemesis    
Fought 100 battles.     

Battle Master    
Fought 500 battles.

Platinum

Neptunia Master System mk2    
It's in your blood…a new strain of Neptunia!    

22 Secret

Bronze

Nepgear mk2    
Nepgear's abilities enhanced.     

Uni mk2    
Uni's abilities enhanced.    

Rom mk2 and Ram mk2    
Rom's and Ram's abilities enhanced.     

CFW Judge, Judged    
Defeated CFW Judge.     

CFW Brave, Humbled    
Defeated CFW Brave.    

CFW Trick, Tricked    
Defeated CFW Trick.     

CFW Magic, Poofed    
Defeated CFW Magic.     

Planeptune Rescue    
Regained Planeptune after its capture.     

Caelus    
Met with Caelus.     

The CPU's Curse    
Obtained the cursed sword of legend.     

Combo Champion    
Achieved an 80-hit original combo.     

Take Off, Every CPU!    
Dealt over 100,000 damage.

Silver

Freshly Grinded Girls    
Everyone reached level 99.   

Normal Ending    
Saw the normal ending.     

Human Ending    
Saw the human ending.     

Planeptune Forever    
Saw the Planeptune ending.     

Leanbox Lover    
Saw the Leanbox ending.     

Lastation Training    
Saw the Lastation ending.     

Lowee's Readership    
Saw the Lowee ending.

Gold

Delphinus Wrecked    
Defeated the secret boss, Delphinus.     

The Blood of Many…    
Finished the Conquest ending route.     

Happily Ever After    
Viewed the True ending.

http://www.ps3trophies.org/game/hyperdimension-neptunia-mk2/trophies/