In Hotline Miami I died a googol amount of times on each level. You have to be super fast, super accurate and plan well ahead to actually finish the levels. I've rage quitted many times from the game.
Dark souls 2 was hard but not impossible. I have played some impossible games of my time but for the life of me I can't think of any right now.
I suppose battle toads would be one of them.
Ghosts ‘n Goblins only once have I ever reach the last level.