The phrase "an increasingly difficult task" is correct and usable in written English.
You can use it when describing a task that is becoming more challenging over time.
Example: "As the project progressed, it turned into an increasingly difficult task to meet the deadlines."
Alternatives: "a progressively harder task" or "a more challenging task over time."
But this too is an increasingly difficult task.
Every new 2D Mario platforming game sets an increasingly difficult task for its designers.
Nerve finds nifty ways to fill the frame, an increasingly difficult task as more and more teen thrillers consist of kids tapping at laptops and staring at phones.
This is an increasingly difficult task, as the proliferation of biennials makes it almost impossible to come up with fresh ideas.
The report noted that the BBC is finding the dual mission of saving money while needing to provide its content on all the platforms consumers use an increasingly difficult task.
The governor of the Bank of England, Mervyn King, is facing an increasingly difficult task of trying to balance relatively high inflation in Britain with the threat that the country's recovery could be hurt by more turmoil in the countries that share the euro.
Take managing foreign currency exposure, an increasingly critical — and increasingly difficult — task.
It is hard to find anyone here in this Palestinian center who does not believe that attacks should continue full force against Israel, even as the United States' special envoy pursues his increasingly difficult task of trying to achieve a cease-fire between the two sides.
These commodity-level players, like the Ourso College of Business at Louisiana State University, are effectively stuck with the increasingly difficult task of trying to distinguish themselves.
Like many other clubs, the Tractor Boys are faced with the increasingly difficult task of falling in line with Financial Fair Play regulations.
As President Obama shifts more fully into campaign mode, he faces the increasingly difficult task of balancing his policy duties as president with his political imperatives as a candidate.
