Castlevania: The Adventure ReBirth
At the title screen, select Game Start and hold right on the d-pad for a few seconds. You'll be able to select and play any levels you have previously reached on the same difficulty.
Contributed By: ShinSageRevival.
Play Style Classic
After playing the game once, you will have the option (in the options menu) to change your playing style to classic.
Contributed By: therealssjlink.