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To unlock Hardcore mode, you must first beat the game on hard mode. Hard mode isn't that much more difficult than say, easy mode. The monsters just have a bit more health and they hit a slight bit harder.
Hardcore is not for the faint of hearts. Since this is a rogue-like, it's going to be extremely luck dependent. It's best to do as much exploring as you can, and make sure to equip a perk that you find is beneficial to your play style.