It's raining hard. You can also say, "It's raining heavily."
Sometimes 'hard' can be an adverb. It is an accepted convention.
To make things confusing, If you say, "It's hardly raining" that means it is raining very lightly, almost not raining.
So, "It's raining hard," has the opposite meaning of "It's hardly raining."
Isn't English crazy?