The phrase "a difficult and vital" is correct and usable in written English.
It can be used to describe something that is both challenging and essential in a particular context.
Example: "The project we are undertaking is a difficult and vital task that requires careful planning and execution."
Alternatives: "a challenging and crucial" or "a tough and essential".
The experience taught me a great deal -- including how difficult and vital the role of a teacher is.
The sharply personal feud over what drugs Ms. Watkins did or did not abuse decades ago was not the only sideshow that allowed the candidates to continue avoiding substantive discussion of arguably the most difficult and vital topic: the city's dire financial picture.
Diderot's efforts as an art writer were based on two complementary beliefs, namely, that the techniques used by a painter to produce various effects are difficult for the ordinary viewer to understand and articulate, and that it is a difficult but vital challenge to capture, through literary language, the significant aspects of a painting.
The need to increase stroke awareness in black, minority and ethnic communities (BMEs) is a difficult, but vital challenge, required to save lives and reduce inequalities.
Finally shedding the last vestiges of colonialism, the region is grasping the fact that it must take a difficult yet vital step into independence and begin to fully manage its own affairs — including military ones.
On the other hand, many signals necessitate a unique and decisive response, and a densely interconnected network may make such signal-exclusivity a difficult but vital objective to obtain [ 6- 8].
The police have a difficult, vital job, to keep society safe.
This is not, it should be said right away, a book without ambition: the subtitle is "Reclaiming Romance for the Twenty-First Century," though it is not exactly romance Nehring is writing about, but a more difficult, vital image of passion she believes we have lost.
But determining the origins of an outbreak that has killed 22 and left 600 people in intensive care presents a difficult mystery to unravel, with vital clues disappearing day by day as contaminated food is thrown away and farm and factory equipment is cleaned.
In a difficult climate, good managers are vital for morale.
