(Note: the question originally asked about "the" before "Millenials".)
Such omissions are not always 'correct' even though they might be grammatical. The definite article and the null article give rise to different levels of specificity. Compare, for example, "I am the king" vs "I am king", or "He is the chicken" vs "He is chicken".
In your case, "Addressing Challenges of the Millennials" is very close to "Addressing Challenges of Millennials", but the version with "the" can give rise to the question, "Which group of Millennials is the author referring to?"
Since you are referring to Millennials in general, the version without "the" would express your intent more unambiguously.
Now, regarding the change in your question to whether "the" should be present before "challenges", it could be argued that exactly the same logic applies: "the challenges" is a concrete set of challenges, while "challenges" without the definite article represents challenges as a quality. However, things aren't so cut and dried with the subject of the clause/sentence. Consider the following:
- The king is here.
- (*) King is here. (note: the asterisk marks an ungrammatical instance)
Unless King is a name, the null article doesn't work here. But if we replace the word King with the word Comfort, it's grammatical again.
Something more is going on. While we might speculate that abstract nouns and names (which can be thought of as an abstract noun) don't require determiners when used as subjects while concrete nouns do, there may be nuances not yet considered here.
However, this gives us just enough to note that with the abstract noun challenges, both forms are grammatical:
- the challenges of millenials
- challenges of millenials
The difference is that including "the" here suggests a concrete set of challenges, whereas the anarthrous form references challenges as an abstract quality.
If you want to clearly announce your intention to address merely a subset of challenges facing millenials, you can use the quantifier "some"
- Addressing Some Challenges of Millenials
This starts to feel a little clunky as a title, but further refinement would take us beyond the scope of this question.