Bronze:

Traditional
Objective: Complete the game using any character.

The Traitor
Objective: Defeat any boss by playing one of his own minions.

Deer Trainer
Objective: Navigate the Abandoned Mill without hitting any obstacles.

Maximum Firepower
Objective: Using a catapult, fling a knight with maximum power.

Animal Handler
Objective: Collect all the animal orbs.

Melee is Best
Objective: Defeat any boss without using magic.

Treasure Hunter
Objective: Find and dig up 10 buried items.

Medic
Objective: In a 4 player game, resuscitate each of your fallen comrades at least once.

Social Networker
Objective: Reach 20 hits in a single Volleyball rally.

Silver:

Kay Eye Ess Ess
Objective: Collect all 4 Princesses' kisses in a multiplayer game.

Conscientious Objector
Objective: Complete the Home Castle through the Barbarian Boss areas without attacking any foes.

Arena Master
Objective: Win 40 Ranked Arena matches

Gold:

You Are Insane
Objective: Complete Insane mode and become the ultimate Castle Crasher.