Wiktionary
n. (context idiomatic English) A challenge with the odds of success stacked strongly against.
Wikipedia
Usage examples of "uphill battle".
Her fight to change that had been an uphill battle from the moment she decided to study at Starfleet Medical Academy in the Federation, but it was not one that Te-Run was likely to appreciate.
I'm inclined to think Governor Street is fighting an uphill battle, even here in his own home state.
It was all rather depressing to Camsan, who'd spent the last half year fighting an uphill battle to teach his tribesmen at least some modicum of caution and discipline, but it was hardly surprising.
I've gotten active through a couple of consumer groups who are fighting an uphill battle to do something about it.
Five horses in front, all still on their feet after the long contest, all intent on the final uphill battle.
It had always been an uphill battle to rouse the public to do what was really in its own best interest.