Boss Rush:
Beat the game with any character once and save. You'll find the new mode at the level select screen.

Crazy difficulty:
Beat the game once as Leon and save. Start a new game and enter the name @CRAZY.

Play as Joachim:
Beat the game once as Leon and save. Start a new game and enter the name @JOACHIM.

Pumpkin sub-weapon:
Beat the game once as Joachim and save. Start a new game and enter the name @PUMPKIN.

Thanks to Revolution readers Bonzie, Fruitbat and surferrosa22!