There are 46 Trophies that can be collected.

Bronze

Tower Defender   
Win a Tower Defense game

Tactician   
Win a Checkers game

Strategist   
Win a Chess game

Captain   
Win a Pirate's Plunder match

Relic Hunter   
Win an Artifact Hunt game

Window Shopper   
Visit the Marketplace

Mechanic   
Visit the Kart & Demo Derby Garage

Housecaller   
Visit another player's house

Barterer   
Complete 5 player to player trades

Icebreaker   
Add a player to your friends list

Groupie   
Successfully invite 5 players to a group

Guildmaster   
Create a guild

Stylist   
Equip a style card

Consumer   
Use a consumable item

Pet Whisperer   
Perform a pet trick

Mime   
Perform 10 emotes

Collector   
Complete a collection

Home Improver   
Place 100 items in a house

Silver

Socialite   
Add 50 players to your friends list

Team Player   
Successfully invite 25 players to a group

Elite Collector   
Complete an elite collection

Master Decorator   
Place 1000 items in a house

Big Spender   
Spend 50,000 coins

Grand Explorer   
Reach Level 20 as an Adventurer

Marksman   
Reach Level 20 as an Archer

Master Blacksmith   
Reach Level 20 as a Blacksmith

Street Fighter   
Reach Level 20 as a Brawler

Iron Chef   
Reach Level 20 as a Chef

Demolisher   
Reach Level 20 as a Demo Derby Driver

Angler   
Reach Level 20 as a Fisherman

Speed Demon   
Reach Level 20 as a Kart Driver

Doctor   
Reach Level 20 as a Medic

Ore Master   
Reach Level 20 as a Miner

Flying Dragon   
Reach Level 20 as a Ninja

Postmaster   
Reach Level 20 as a Postman

Striker   
Reach Level 20 as a Soccer Star

Warlord   
Reach Level 20 as a Warrior

Arcane Master   
Reach Level 20 as a Wizard

Gold

Celebrity   
Add 100 players to your friends list

Platinum

Free Realms Champion   
Earn all trophies

6 Secret

http://www.ps3trophies.org/game/free-realms/trophies/