It means when you are determined to do something, similarly like Bruce Willis in the film Die Hard.
Can be used as a verb or a noun.
Boy 1: Lets ride into town
Boy 2: Yeah come on, lets go quick-time
Boy 3: Theres no point die-harding it up, might as well take our time.
Boy 1: Whoa look at him, climbing that mountain with no gear
Boy 2: Yeah I know he's a right fuckin die-hard.
*Boy 1 shoots Boy 2*
*Boy 2 manages to get to his feet and crack Boy 1 in the jaw before dieing*
Boy 3: Die hard.