"eminent challenges" is correct and usable in written English.
You can use it to refer to significant difficulties or tasks that must be faced and overcome. For example, "The project was filled with eminent challenges, but we ultimately prevailed."
The way these molecules work depends on how the strings fold, but calculating the folding is, as the Foldit researchers put it, "one of the pre-eminent challenges of biology".
Healing these divisions is the pre-eminent challenge of our time if we are to create a post-Brexit future for our country that offers hope to all.
History has recorded, however, that our great nation did not keep its word to the Indian nations, and our pre-eminent challenge today...is to assure the integrity of our treaty commitments and to bring an end to the era of broken promises".
The ineffable nature of spirituality was a pre-eminent challenge, both in terms of articulating their views in the study and in relation to addressing spiritual issues in the clinical encounter, supporting the findings of previous studies and theoretical frameworks.
Our own pre-eminent moral challenge will be to ease the brutality that kills and maims girls and women across much of Africa and Asia.
The GRD would confer no right of participation in decisions over the use of natural resources as the dividend would be akin to preferred stock and would not challenge eminent domain.
This documentary theory of the composition of the Pentateuch has been challenged by eminent 20th-century scholars who have offered alternative or additional methods of analysis and interpretation.
But others, among whom I imagine Sartre would have been pre-eminent, would have challenged the asseveration on a deeper philosophical level.
Then, as luck would have it, after a work by Gerhard Richter sold at auction for a staggering $34.2 million, along came a challenge on Facebook proposed by Jerry Saltz, eminent art critic for New York magazine, which challenged artists to produce a painting in a perfect Richteresque-style for just $155, and Saltz would come for a studio visit.
James Joyce once confessed, with puckish pride, that "Finnegans Wake" would "keep the professors busy for centuries," and a similar challenge is issued, to eminent scholars of pop culture, by "Ready Player One".
The people of San Salvador Atenco formed a group called the People's Front in Defense of the Land, or FPDT in Spanish, to challenge the government's eminent domain.
