To start a save file in hardcore mode:

1. Beat a file and unlock hardcore legit.
2. Select hardcore in that file
3. Go back to the menu and select a new file (or even any file without hardcore unlocked).

You should now be in hardcore from the start. You can tell because when you enter the first level you get an achievement for entering a level in hardcore.

This works for reverse too but level 1 is unbeatable in reverse without any powerups so it's pointless