What part of speech is "fun" in “Hiking is fun”?
In the sentence "Hiking is fun," the word "fun" is an adjective. It's the same type of construction as, for example, "My mother is tall."
The word "fun" can be a noun as well as an adjective, and the verb "is" can link two nouns ("My mother is a teacher"), so I can see where you might be confused. But in the sentence "Hiking is fun," most English speakers would understand "fun" as an adjective, almost as if it were shorthand for "Hiking is a fun thing to do."
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.
In the given example, 'fun' can be either a mass noun or an adjective, because either can function as the predicative complement of the copula 'is'. Thus, you'd have to dig deeper to figure this out.
The Cambridge Grammar of the English Language (Page 1643) says that the word 'fun' is originally a noun but is recently also used as an adjective, especially among younger speakers:
To establish that a noun has been converted into an adjective we need to show that it has acquired distinctively adjectival properties. Since the ability to modify a noun is not restricted to adjectives this will normally mean showing that it has become gradable and takes the distinctive degree modifiers that are found with adjectives but not nouns, notably very and too. One often-cited example is fun (and the fact that this example is cited so often reflects the paucity of clear examples): many speakers, especially younger ones, accept expressions like a very fun person, indicating that fun has been assimilated into the adjective category.