There are 12 Trophies that can be collected.

Bronze

The Spark
Win a game

Life Preserver
Increase your life total to 30 or more in single player, or 60 or more in Two-Headed Giant

Magic: The Puzzling
Complete a challenge

Devastator
Deal 20 combat damage to a player in a single turn in a game

Defender of Foriys
Win a Two-Headed Giant game

Spellslinger
Defeat someone who has earned the Spellslinger trophy

Duelist
Win 5 ranked PlayStation Network matches

Silver

Epic Conclusion
Defeat Tezzeret in the final single-player campaign battle

Puzzling Master
Complete all challenges

Master of Artifice
Defeat Tezzeret the Seeker & Sarkhan Vol in the cooperative campaign

Duels Master
Win 10 PlayStation Network matches

Gold

Planeswalker
Unlock 100%

http://www.ps3trophies.org/game/magic-the-gathering-duels-of-the-planeswalkers/trophies/