Here is the list of trophies you can achieve for DC Universe Online for the PS3.
Acrobatic Ace (Gold) – Achieve level 30 as an acrobat
Champion of Earth (Gold) – Achieve level 30 as a hero mentored by Superman
Criminal Mastermind (Gold) – Achieve level 30 as a villain mentored by Lex Luthor
Fearless Flier (Gold) – Achieve level 30 as a flyer
Knight for Justice (Gold) – Achieve level 30 as a hero mentored by Batman
Mission Control (Silver) – Achieve level 10 and gain the Controller Role
Platinum Pace (Gold) – Earn a platinum medal in any race
Speedster Supreme (Gold) – Achieve level 30 as a speedster
Tanks Very Much (Silver) – Achieve level 10 and gain the Tank Role
The Healing Touch (Silver) – Achieve level 10 and gain the Healer Role
The Joker in the Deck (Gold) – Achieve level 30 as a villain mentored by the Joker
The Queen’s Favorite (Gold) – Achieve level 30 as a villain mentored by Circe
Warrior of Truth (Gold) – Achieve level 30 as a hero mentored by Wonder Woman
Winner Takes All (Platinum) – Acquire all hero and villain trophies in the classic game