"extraordinarily fierce" is correct and usable in written English
You can use it when you want to emphasize that something is especially fierce and/or intense. For example, "The wind was extraordinarily fierce and caused the trees to sway violently."
The Tigers, as they were known, were extraordinarily fierce.
That battle could be decisive militarily and extraordinarily fierce, he said.
The rallies underscored the unusual passions being aroused by the campaign, in which the leading candidates have exchanged accusations that are extraordinarily fierce for Iranian politics.
The face of Hong Kong's biggest action star is extraordinarily sharp and fierce, almost feral, with eyes, nose and chin formed like some kind of nunchuck or martial arts weapon.
He was beaten by the sweet venom of a Rooney shot in the 34th minute, but if we thought this a fierce strike of the ball, something extraordinarily more powerful was to come.
Sharp, extraordinarily long claws at the tip of each leg suggest the spiders are fierce predators, but what they prey upon and how they capture it are currently unknown, the researchers report online today in ZooKeys.
*All of this taking place in a fierce new political world where the collapse of party discipline has made it extraordinarily hard for officials on Capitol Hill, let alone for a president, whether of their party or not, to lead.
It had been an extraordinarily eventful last round in which his game, rather like that of Rory McIlroy in this year's Masters, had started to wilt in the fierce glare of the spotlight.
The saddest cases, the counselors tell me, involve extraordinarily well-educated people -- men and women with Ph.D.'s and law degrees -- who have propelled themselves into an elite stratum where job competition is still fierce.
