The phrase "a difficult set of" is correct and usable in written English.
It can be used when referring to a collection of items, tasks, or challenges that are complex or hard to manage.
Example: "The project presented a difficult set of challenges that required innovative solutions."
Alternatives: "a challenging group of" or "a tough collection of".
The river presents a difficult set of reclamation problems.
Still, the officials had a difficult set of options.
It involves a difficult set of technical judgments about the functioning of voting machines.
I don't see us muddling through a difficult set of economic events.
"Our officers deal with challenging situations every day and in this case they responded to a difficult set of circumstances.
"The Kraut, caviar, and champagne," Hemingway said slowly, as though he were memorizing a difficult set of military orders.
Žuran and colleagues' study is an interesting clinical observation made in a difficult setting of clinical practice treating patients with sepsis and organ failure, for which the authors ought to be congratulated.
"I think he's fighting a tough battle under a very difficult set of circumstances where every little flaw or misstep is magnified by the media, while the bumbling mistakes on foreign policy and otherwise being committed by the administration are papered over by that same media," Bauer said.
She has done a very good job in a very difficult set of circumstances with the Leveson inquiry that has stirred up a lot of media antipathy to her. "And also the gay marriage stuff – there are a lot of Conservatives out there who, perhaps, were not necessarily in support of it all and so feel rather bitter about that.
Initially, they gave both groups of students a fairly difficult set of ten questions from a nonverbal IQ test.
It's a very difficult set of circumstances.
