These must be beaten in Championship Mode:

• Mr. Garrison - Defeat Rally Days #2
• Mr. Mackey - Defeat Spring Cleaning
• Big Gay Al - Defeat Pink Lemonade
• Mephesto - Defeat 4th of July
• Grandpa - Defeat Halloween
• Jesus - Defeat Christmas
• Satan - Defeat New Year's Day
• *Ned - Defeat 4th of July with Kyle
• *Damien - Defeat Halloween with Kenny

Various Other:

• Visitor(Alien) - Grab 2 Pot Pies on Memorial Day.
• Ike - Grab the cheat item on the airplane wingtip on Memorial Day.
• Terrance & Phillip - Grab 4 gold cows on Christmas.
• Random Track Select - Defeat the entire Championship mode.

*I belive this is a random track select to give you a hidden character depending on which character you are using.