There's little evidence for saying that "fun" is an adverb, but a case can be made for it being either a noun or an adjective. Evidence for it being a noun or adjective would be that it is possible to say either of the following:
Hiking is such fun (and championship).
Hiking is so fun (and exhilarating).
whereas generally when the category of the word is less controversial, such specifies nouns, not adjectives, and so specifies adjectives, not nouns:
*Hiking is such exhilarating/tiring.
*Hiking is so drudgery/championship.
So the answer is essentially that the speaker can make it either a noun or an adjective.