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

ARRR! (Bronze): Complete "Plundering Pirates" episode.
NI! (Bronze): Complete "Naughty Knights" episode.
10 in a Row (Bronze): Complete 10 Levels in a row.
25 in a Row (Bronze): Complete 25 Levels in a row.
500K Plan (Bronze): Score 500,000 points.
Millionaire's Club (Bronze): Score 1,000,000 points.
The Morris Award (Bronze): Gain 9 extra lives.
Bonus Plan (Bronze): Collect 200 "Bonus Points" power-ups.
Minuteman (Bronze): Complete a level within one minute.
Back in the Chain Gang (Silver): Start a chain reaction with a bunch of cannons.
Through the Fire and Flames (Silver): Seek out and aid the lone knight in his fight against the dragons.
Award Winner (Gold): Collect all Awards in the game.

Additionally, there is one secret trophy:

Goodbye Cruel World (Bronze): 5 Killer Skulls collected.

The following trophies require the "Wicked Witches" bonus downloadable content:

50 in a Row (Bronze): Complete 50 Levels in a Row.
As You Wish (Silver): No one should hinder true love. Find the lovers and make those around them go away.
EE-HEE-HEE-HEE-HEE-HEE!!! (Bronze): Complete "Wicked Witches" Episode.
Evening Exorcist (Silver): An evil witch performs dark rituals. Put an end to them by destroying her at nighttime.
More Points Than You’ll Ever Need (Bronze): Score 2,000,000 points.