There are 50 Trophies that can be collected.

BRONZE

Fusion Expert
Perform 50 Persona fusions

The Nose Doesn't Always Know
Experience a fusion accident

Persona Shopper
Buy a Persona from the Compendium

A Favor for Marie
Register a Skill Card

Card Collector
Register 100 Skill Cards

Displaying Adaptability
Switch Personas 5 times in 1 battle

Hardcore Risette Fan
Hear 250 of Rise's navigation lines

Going Nova
Deal over 999 damage in 1 attack

Skilled Commander
Perform 50 All-Out Attacks

Tactical Fighter
Exploit enemy weaknesses 100 times

Fill Your Hand
Get 50 Sweep Bonuses

Grasping at Greed
Defeat a Golden Hand

Food Fighter
Finish Aiya's special dish

Compulsive Reader
Read all books

It's Working Today
Buy an item from the Capsule Machine

Lucky Me!
Win a prize from the vending machine

Granter of Your Desires
Buy 5 things from Tanaka's Amazing Commodities

Seize the Moment
Buy a special croquette from Sozai Daigaku

Cooking With Gas
Make 5 perfect boxed lunches

A Special Lady
Enter a special relationship with someone

The Other Self
Obtain the Persona Izanagi

Fashion Plate
Fight a battle in costume

Head of the Class
Rank #1 in your class on an exam

Fishing Master
Catch the Sea Guardian

A True Bond
Max out a Social Link

Bond Maniac
Max out 10 Social Links

An Acquired Taste
Drink the coffee at Chagall Cafe

Movie Buff
Go to 3 movies at 30 Frame

Bug Hunter
Swing the net with perfect timing

Advantage Mine
Enter a battle with Player Advantage

A New Quiz King
Win the Miracle Quiz Finals

SILVER

Mr. Perfect
Max out all social qualities

Moderate Bookkeeper
Register over 50% of the Compendium

Legend of Inaba
Max out all Social Links

GOLD

Thorough Bookkeeper
Complete the Persona Compendium

PLATINUM

Golden Completed
Earn all trophies

14 SECRET

BRONZE

A Prince Appears
Rescue Yukiko Amagi

A True Man's Stand
Rescue Kanji Tatsumi

The Lounge Is Closed
Rescue Rise Kujikawa

Game Over
Secure Mitsuo Kubo

Boarded-Up Lab
Rescue Naoto Shirogane

The Return of the Angels
Rescue Nanako Dojima

Breaking Through the Fog
Secure Tohru Adachi

Special Fusion Expert
Use 4 or more Personas in a special fusion

Big Bro is Worried
Visit Nanako in the hospital 3 times

SILVER

Welcome Back
Rescue Marie

The Reaper Becomes the Reaped
Defeat The Reaper

The Power of Truth
Create Izanagi-no-Okami

GOLD

The Truth In Your Hands
Defeat Izanami

One Who Has Proven Their Power
Defeat Margaret

http://www.ps3trophies.org/game/persona-4-golden-en/trophies/