hard work or hardwork

[Harold Medina]

Which is correct? hard work or hardwork?

[English Freak]

Welcome to the forum.
"Hard work" is correct. "Work" is a noun here (an uncountable noun).
And we have "hard-working" too which is an adjective, as in a hard-working nurse.

[BobK]

Which is correct? hard work or hardwork?

But you were right to ask. There are many composite words that end '-work' - like 'firework', 'woodwork', 'homework' ...etc. In all those cases, the first part is a noun; but some adjectives do this too. In this example there's a spelling change, which makes the join between the component words less obvious: when you produce a piece of work that shows how handy you are, that is 'handiwork' (maybe a bit archaic, but certainly in current use, often in collocation with 'admire': 'When he had finished ....<doing-whatever>... he stepped back to admire his handiwork.')

b