An enemy have variable life = 50 in normal dificulty
at hard dificulty you can multiply or add more life to the enemy
the same for anything that make it harder, if it's a RPG then damage will be higher, etc.
if global variable difficulty = 3 (harder)
then set enemy life = 10 * global variable difficulty
then the enemy will have 30LIFE.
if it's on easy difficulty
it will be 10 * 1 = 10.
You can also make the layout harder.. example: you have a plataformer game.
in normal difficulty there's 2 platforms to jump.. at harder dificulty there's only 1.