Hard as hell means very difficult or painful, emotionally:
The examination was hard as hell.
Losing a friend is hard as hell.
Hard is a common word for difficult in English, including practical, mental, and emotional difficulty:
It’s hard to learn physics.
Poverty is a hard life.
You may know that hell is the opposite of heaven in Christianity—where bad people go after death. Therefore, hell is the most negative place possible, so when we want to say very, very bad, we can use as hell or like hell:
I’m tired as hell.
That painting is ugly as hell.
Like hell I will! (= I will not!)
Hell can also be used as an intensifier—like the word very—for positive things sometimes:
That dog is cute as hell! (that dog is very cute)
That’s a hell of an idea! (that’s a great idea)