The Culture subsection of the Oxford Advanced Learner's Dictionary's entry for "campus" begins with
The popular image of student life is of young people with few responsibilities enjoying themselves and doing very little work. This is often not true.
Why didn't it say "the student life" or "a student life"?
The popular image of student life ...
The noun life does not refer to a specific instance of life, but rather life in general.
Keep in mind that life here is actually part of a prepositional phrase which combined serves to qualify image. The sentence talks about an instance of an image and therefore that has an article.
It seems there are some grammatical considerations here that you already understand.
The word "life" can be uncountable or countable depending on whether general concepts ("the meaning of life") or a specific example ("This is the life!") is meant. That distinction holds for most of the word's different senses, including those for "a course, condition, or manner of living" that cover how students live their lives.
Separately, both "a" and "the" can be used to refer to classes of things. Without other context, saying "A student enjoys themself, having little work and few responsibilities" and "The student enjoys themself, having little work and few responsibilities" convey the same 'information' about the referent, some generic student. The emphasis is a little different and (for the reasons discussed here) make the second one sound obnoxious to most people raised in the Anglosphere.
As Mr Clifford's answer discussed, it may be that you're still uncomfortable with adjectival use of nouns. The word "student" in your sentence is not talking about a particular student or even a generic one; it is simply limiting the noun "life" to discuss specifically the manner of living shared by students. It's grammatically correct. Taken as the general concept of "student life", it remains uncountable and no article is needed.
Your confusion about needing articles may come from either of two concerns.
If Mr Clifford was right that you misunderstood attributive nouns, it may be that you wanted the word "student" to be acting as a noun talking about particular people instead of as an adjective limiting the kind of life under discussion. In that case, neither of your suggestions would work. You can talk about the life of a representative student or the life of the generic student, but you need to use the possessive form to keep "student" as a separate noun: "the popular image of a student's life is..." or "the popular image of the student's life is..."
However, it may also be that you're a bit uncomfortable with countability. If you think that using "student" to modify "life" makes it a special kind of life that might require an article, that's a separate issue. The first thing to realize is that, if "student" is just an adjective modifying "life", any article that you add in front of it will be too. The second thing to realize is that because the countable meanings of "life" are marked by the presence of articles, it becomes ambiguous and awkward if you try to use "a" to discuss classes of the uncountable meanings instead.
In other words,
Student life isn't all wine and roses.
and
The student life is not all beer and skittles.
A student's life ...
The student's life ...
are largely equivalent. The first is more comfortable, feels shared, and better suits the plural continuation of your sentence. The second isn't wrong but feels more as if a contrast is being drawn with some other mode of life and (as discussed here) makes the speaker seem more judgmental, possibly even obnoxious. All three would be better served by rephrasing the following idea of your sentence singularly or impersonally.
A student life is ...
a bit off. Even more than "the student life", it should have a singular continuation of your sentence. It also really needs to used in a particular context contrasting it with other modes of life to feel appropriate and get away from referring to the other countable ideas (the nondead status of a student, the life force of a student, the biography of a student, &c). You still see it in the wild—"A Sailor's Life", "A Pirate's Life for Me!", "A student life is a golden life"—but it's much, much less common.
In this case "student" is a noun adjunct modifying "life" to elaborate on what kind of life is being talked about. Without it, it becomes
The popular image of life is of...
which means something different but sounds fine. It wouldn't sound right if you added articles, because then without the noun adjunct you'd either be saying
The popular image of the life is of...
or
The popular image of a life is of...
which both sound off because you're talking about life in general. You don't mean an individual person's life, so articles aren't used.
