Way of the Strong is the difficulty that unlocks when you've beaten the game for the first time. It is effectively the game's New Game Plus.
Way of the Strong
When you've defeated the game, upon returning to the general overview screen you can select any of the Missions available and choose Way of the Strong as their difficulty. Like Twilight Missions, this new difficulty is much tougher but the rewards for completing them are much higher than other difficulty levels.