Acquire the Mystic.

Get all other trophies in the game

Defeat Purple Tentacle yesterday

Acquire a diamond

Power Hoagie's Chron-o-John

Red makes a super battery with only a little help from Hoagie

Power Laverne's Chron-o-John

Laverne thinks about eating the cat

Make vinegar

Wake up Dr. Fred

Try to sign the contract yourself with the quill pen

Talk to Washington, Jefferson, or Hancock while they're outside