Unfortunately for whatever reason the game never preserves the difficulty for the Art of War scenarios, however there is only one way to play on Hard difficulty.

1. Pick a scenario on Hard difficulty on any campaign but Art of War.
2. Quit to menu and then quit the game.
3. Now pick the Art of War scenario you want to play. After this the game will always put you on Moderate for Art of War and you have to redo the steps above again, which is very time-consuming.