'fierce scrutiny' is a correct and usable phrase in written English.
It is often used to describe an intense level of close examination or evaluation. For example, "The new policy was subjected to fierce scrutiny before it was approved by the board."
Coming off another week of fierce scrutiny, the Tigers predictably came out hard.
Above all he will have to get used to fierce scrutiny.
This decision (like all rail franchising decisions) was always going to be subject to fierce scrutiny.
As the administration's national security policy has come under fierce scrutiny, however, it has been raised along the margins.
This could provide Stones the mental strength required to deal with the fierce scrutiny that will come if he is to be the key factor the manager wishes.
But the collapse brought the Buildings Department, which oversees construction work in the city, under fierce scrutiny and led to the resignation of its commissioner, Patricia J. Lancaster.
In Daisey's defence, it would be surprising if every detail in the monologues of the late Spalding Gray – including Monster in a Box and Swimming to Cambodia – survived the fierce editorial scrutiny Daisey has latterly faced.
As Facebook continues to face fierce media scrutiny over how it handles user data, the company may well be wishing for some gentler headlines.
But fierce ongoing scrutiny of the issue has brought to light a number of contacts, including some involving members of Trump's own family.
It's worth pausing to note that CAGE has come under fierce media scrutiny in the past, and some human rights organizations including Amnesty International UK have distanced themselves from the group.
All this is warming up nicely, with Catherine under fierce internal-affairs scrutiny, Royce giving it great pink-eye in prison when told by an inept vicar of his mother's fate, and the ever-watchable Shirley Henderson turning up as one of those souls who fall, bless, for convicted women-haters.
