"by extraordinary" is correct and usable in written English.
You can use it in the context of emphasizing the unusual nature of an event or outcome. For example, "The play was a success by extraordinary measure."
Bishop Jin's life was marked by extraordinary political conflict.
But the movement has been marked by extraordinary untainted enthusiasm.
These are extraordinary words, perhaps justified by extraordinary times.
"I was taught by extraordinary people," he remembered.
"Maples was disarmed by extraordinary circumstances quite beyond his control," Justice Ginsburg wrote.
His vocal tone is made by extraordinary resonance between the cheekbones, now buzzing, now humming.
Their incomes rose by extraordinary levels, but so did the price of the goods they buy.
His powers of invention were matched by extraordinary energy and versatility.
But, he added, he was "motivated to do large short positions by extraordinary circumstances".
Yet the two most successful spies, Maclean and Philby, were inspired and supported by extraordinary women.
By extraordinary fortitude, the Sikh family made it to Britain, hoping to find safe haven.
