You should accomplish the task to unlock the following:
Hades Card: Defeat Hades
Jafar Card: Defeat Jafar
Tinkerbell Summon Card: Defeat Captain Hook
Firaga Break: Use Calm Bounty in Twilight Town
Stop Spell: Use Calm Bounty in Wonderland
Shock Impact Skill: Use Calm Bounty in Atlantica
Fire Raid: Use Calm Bounty in Halloween Town
Cloud summon card: Defeat Hades
Genie Summon Card: Defeat Jafar
Dragon Maleficent Card: Defeat Maleficent
Riku Card: Defeat Riku IV
Ursula Card: Defeat Ursula
Captain Hook Card: Defeat Captain Hook
Darkside Card: Defeat Darkside
Gravity: Use Calm Bounty in Agrabah
Blizzrad Raid: Use Calm Bounty in Olympus Colleseum
Dumbo summon card: Complete 'Monstro' level
Simba Summon Card: Meet Leon for the first time
Bambi Summon Card: Lead Pooh to the end of 100 Acre Wood
Lionheart: In Traverse Town use the key to rewards
Metal Chocobo: In Collisieum use key to rewards
Blazing Donald Skill: Open Key of Rewards Door in Agrabah
Water Splash Skill: Open Key of Rewards Door in Monstro
Gravity Raid Skill: Open Key of Rewards Door in Halloween Town
Stop Raid Skill: Open Key of Rewards Door in WonderLand
Thunder Raid Skill: Open Key of Rewards Door in Neverland