"unflinching approach" is correct and usable in written English.
You can use it when you want to convey that someone is taking a determined, resolute, and stern course of action. For example, "The board of directors took an unflinching approach when deciding to reduce staff to save money."
Manet's daring, unflinching approach to his painting and to the art world assured both him and his work a pivotal place in the history of modern art.
In the mid-90s, Holt served as chairman of the Arts Council Drama Advisory Panel, antagonising the grey, male-dominated bureaucracy with her unflinching approach.
Indeed, several officers interviewed applauded the mayor's unflinching approach, calling it a brave stance in an era when many politicians pandered to police critics.
But there was a nervousness among some senior Tories that Osborne had abandoned the last vestige of compassionate Conservatism and bet the farm on such an unflinching approach to the deficit.
Pearson, who has appeared at every Paralympics since Sydney 2000, said huge strides had been made and that he would welcome an unflinching approach to the presentation of sport and disability in London.
Danish director Thomas Vinterberg's own experiences of growing up in a commune during the 1970s and 80s inform his unflinching approach to the subject in this drama, which was based on his own stage play, Kollektivet.
Es has an unflinching desire to approach theatre in an almost musical fashion beyond the restrictions of naturalism.
Coetzee's approach is unflinching and subtly fierce, but always much more oblique, avoiding specifics of location and landscape.
Prominence and use generates student discussion; we believe that is why the ELSIs are likely to succeed and are an unflinching part of the approach taken in ICB they are not an afterthought or simple enrichment exercises.
Wigglesworth's highly energised approach suits the unflinching directness of the staging – orchestrally and chorally the performance is high-class.
From a distance, I could see the Egyptian military guard scrutinizing my two daughters and me, taking in our knee-length skirts, unveiled heads, saying nothing as Daniel approached, his brow unflinching under a stiff wool beret.
