There are 12 Trophies that can be collected.

Bronze

Apple of My Eye
Win your first online game.

Sour Apple
Play a Golden Apple Card for the first time.

Mad Apple
Lose 3 online games in a row.

All Your Apples Are Belong to Us
Play the "Apple Tart" card 10 times.

No Apple for You
Play the "Yes, We Have No Apples" card 10 times.

Apple Seeds
Complete the tutorial in Single Player.

Social Addict
Enable Social Integration for posting trophies.

Silver

Apple-opolis
Unlock all the Apple Avatars.

Rotten to the Core
Be targeted by the "Rotten Apple" card 10 times.

Falling Far from the Tree
Play the "Every Apple for Himself" card 5 times.

Apple-ocalypse
Be the second player to play the "Upset the Apple Cart" card in a single round.

Gold

An Apple a Day
Reach the Orchard Rank in Online Multiplayer by Playing 500 Games.

http://www.ps3trophies.com/forums/playstation-trophy-news/8388-apples-apples-trophy-list.html