Elephant Finnick (Zootopia): complete the Masters of Disguise set to unlock Elephant Finnick. This set can be completed in any order that you want to. Once you complete it, Elephant Finnick unlocks automatically.
Chip (Mickey and Friends): When you complete the Crazy Critters set, you can earn the bonus character Chip. Complete the set in any order to unlock Chip automatically once you finish the level.
The Prospector (Toy Story): Complete the Toy Story 2 set and you will unlock The Prospector once the stage is done. This set consists of Emperor Zurg, Wheezy, Baby head, Trixie and Janey Doll.
Fred (Big Hero 6): Unlock the Best Friends set. This consists of Hiro Hamada, Go Go Tamago, Honey Lemon, Baymax and Wasabi. Once you have all of them, you get Fred.
Alistair Krei (Big Hero 6) Complete the Top Dogs set to unlock Alastair Krei. Most likely this consists of all of the big bads from the other Disney worlds in the game.
The Cat Lady (Haunted Mansion): Complete the Leading Ladies set to unlock the Cat Lady. Once this whole set is done, then you will unlock The Cat Lady automatically as soon as you finish the level.
The Giraffe (The Lion King): Complete the Big and Tall set in order to unlock the Giraffe character. Look for the big characters (Adult Simba, Nala, Pumbaa, Ostrich) to complete this set.