Here's what you can do:
1. If you so choose, store your money and any items you want to keep. (Alternatively, you could just continue playing as you would on Heroic, but once you die, continue with step 2 here instead of just continuing the same character.)
2. From the title screen, choose "NEW GAME". Then select your file.
3. You'll be asked for confirmation, then you will go through the same menus as when starting a new game, including the option to choose a new difficulty.
Alternatively, the "MANAGE DATA" option (I think that's what it's called) allows you to delete just the character data from the slot, and then you can just start a new character on Heroic by just loading the save.
(This method is also the only way to go back to first playthrough mode if you're on New Game + or Savage World on the Adventure setting. To be honest, New Game + is not that great if you're already level 20 (requires DLC1), but Savage World manages to be a good challenge at that level.)
