'daunting mission' is correct and usable in written English.
You can use it to refer to a difficult, challenging, and intimidating goal or task that a person has to face. For example: The firefighters accepted the daunting mission of rescuing a family from a burning building.
They were familiar characters dropped into a familiar setting, tasked with a familiar, if daunting, mission: save the world.
Hammond spoke as the defence secretary, Michael Fallon, warned that Britain and its allies are facing a daunting mission to destroy Isis that could endure for as long as three years.
Gordon Brown last night appeared to have failed in his daunting mission to change the course of the general election during an ill-tempered leaders' debate in which he repeatedly rounded on David Cameron and warned that Conservative spending cuts would imperil the fragile recovery.
He faced a daunting mission.
Its daunting mission is to take on the Google juggernaut.
Trying to recapture faded pop desirability is a daunting mission for any brand.
He also laid blame on world leaders, including Clinton, for indecision and not providing sufficient resources to tackle daunting peacekeeping missions that had already spread U.N. soldiers across the globe.
Even some agencies ranking relatively high on the OPM survey, moreover, simply don't have the management and manpower in place to handle the daunting new missions coming their way.
But his mission proved daunting.
The UN's Secretary General Ban Ki-moon said his mission was "daunting, but not insurmountable" and called for "a unity of effort that will have an impact on the ground".
After all, she's embarking upon a mission that may be daunting, but it is well within reach: To become the first New Yorker, male or female, to break into modern competitive surfing's top tier.
