Games that are more skill based and want to encourage player improvement will stress that this difficulty is gruelling, but not impossible, and that you will need to bring your best skills forward if you want to succeed. How 'fair' this difficulty mode is depends on the game. Oftentimes this is unlocked by beating the game on the lower 'hard' difficulty. If the game describes how each difficulty mode works, its explanation will often be an inversion of Surprise Difficulty, in that the game makes clear just how hard things are going to get. To qualify for this trope, the difficulty level needs to be above any lower existing 'hard' difficulty, and of course, be extremely difficult.
Harder Than Hard mode is a Difficulty Level that's exactly what it sounds like: a mode intended only for the most skilled players who are looking for the toughest challenge the game has to offer.