The word "unconquerable" is correct and usable in written English
You can use it to describe something that is too strong or powerful to be defeated or overcome, or to describe someone's determination or spirit in the face of overwhelming odds. For example: Despite the odds, she remained unconquerable in her determination to achieve her dream.
For a start, its remarkable "tension-leg" design allows it to sit safely atop 3,800 feet of treacherous water a depth thought unconquerable only a few years ago.
"We are blamed as criminals and seen as human beings of a lower order that cannot subject its passions to reason...as natural-born, promiscuous carriers of germs, unique in the world, doomed to a mortal end because of our unconquerable devotion to the sin of lust," he said.
Afghanistan, remember, was the unconquerable natural fortress and the graveyard of the Soviet empire.
Their leadership is headquartered in Pakistan, which makes them unconquerable.
Thabo Mbeki, South Africa's president, once complained that: "We are blamed as criminals and seen as human beings of a lower order that cannot subject its passions to reason...as natural-born, promiscuous carriers of germs, unique in the world, doomed to a mortal end because of our unconquerable devotion to the sin of lust".
It was Muḥammad Aḥmad who converted this diversified discontent into a unified movement that for a time would transcend tribalism and weld the faithful into an unconquerable military machine.
Despite constant money problems, he maintained, as George Bernard Shaw said, "an unconquerable gaiety of soul" that sustained him, and he was visited by such loyal friends as Max Beerbohm and Robert Ross, later his literary executor; he was also reunited with Douglas.
They were attacked on philological grounds by such iconoclasts as Thomas R. Lounsbury; they were reduced to vanity by the unconquerable speech habits of the folk.
In this defeat Washington displayed the combination of coolness and determination, the alliance of unconquerable energy with complete poise, that was the secret of so many of his successes.
The poem, which he read in prison and much later at the funeral of one of his sons, begins: "Out of the night that covers me,/ Black as the Pit from pole to pole,/ I thank whatever gods may be/ For my unconquerable soul".
But, once the excitement of lighting an ancient gas stove with a match had worn off, I discovered the aching hunger — unconquerable by even the largest plate of spaghetti and entire bottles of Communist reds — that is peculiar to eating too often alone.
