There are 12 Trophies that can be earned in this title.

Bronze

Elhorn Tourist
Completed all stages

Zephyrus Saviour
Completed Arcade Mode on Normal

Ferocious Flier
Completed 1.2 having defeated all enemies

Wolf Connoisseur
Completed 2.1 having collected all pickups

Nimble Knight
Completed 3.2 without taking damage

Burst Friends
Defeat 5 enemies in a single Rocket Burst or Drill attack

Woodland Bouncer
Defeat 3 enemies with a single reflected projectile

Silver

Devotindos Defiler
Completed Arcade Mode on Hard in a Single Playthrough

Impatient Hero
Completed all stages below par time

Spark Dog Millionaire
Completed Arcade Mode scoring One Million Points or more

Redoubtable Runner
Completed Arcade Mode on Hard within 60 minutes

Gold

Legendary Possom
Completed Gold Sparkster Mode

http://www.ps3trophies.org/game/rocket-knight/trophies/