Expert Mode is actually the hardest mode in the game. You have to go through all the stages without dying. Keep lives of a minimum to 30. Best way to go. Even "The Last Way" you have to do. Like I, myself have beaten Expert Mode. It took 6 hours for me to complete.
To unlock Expert Mode,
1: Make sure you beat every stage.
2: Get all A's in every stage.
NOTE: Space Gadget has a Normal mission, so once you are at the emerald, let Hero Mission fail, and get the emerald. You WILL get an A at that.
There are 71 A's you have to get.
Good luck!