Successfully complete one of the following tasks to get a trophy:

JUMP! - Landed! (Bronze): Complete the Adventure Mode.
JUMP! - Treasure hunter (Silver): Complete the Challenge Mode.
SWAP! - Claim your castle! (Bronze): Achieve the Castle mode.
SWAP! - King of my castle (Silver): Score more than 60,000 points in Arcade mode.
SWAP! - Unchallenged (Silver): Complete all the challenges.
SWAP! - Treasure hunter (Bronze): Collect 1,000 treasures.
PIXEL! - Coming home (Silver): Complete all the levels.
PIXEL! - That (Silver): Collect all the Useless Relics.
PIXEL! - Fearless tomcat (Bronze): Kill 1000 foes.
PIXEL! - Magnificent (Bronze): Achieve all the hidden pixel mini-games.

Additionally, there are four secret trophies:

JUMP! - Diehard (Bronze): Achieve 10 levels without dying.
JUMP! - On target (Silver): Kill 25 foes with the knife.
SWAP! - Maxi-match (Silver): Match a 10 bricks shape.
PIXEL! - Broken ground (Bronze): Destroy 200 breakable blocks.