"engage critically" is correct and usable in written English.
You can use it to encourage someone to think in-depth about a particular subject. For example, "Engage critically with the text to discover its deeper meanings."
Because few critics are willing or able to engage critically with the movie on race, McDonagh himself does not have to engage, does not have to wrestle with some of his failures as an artist.
It's strangely difficult to engage critically with such a piece.
Her reluctance to engage critically with Wright's work is particularly unfortunate.
By the time she graduated, she had discovered her talents as a researcher and writer and was excited by the chance to engage critically with Britain's role in the developing world.
"In the wake of Contagious Diseases Act, there was an opportunity to engage critically with the issue of the regulation of prostitution and a feminist debate around this too, which might have added a really interesting dimension to this," says Harris.
We observe few instances of citations that engage critically with Schön or build on his ideas.
Other film-makers have engaged critically with The Birth of a Nation.
Engaging critically with history is precisely what the campaigners are undertaking.
But also someone who understood that the challenge of engaging critically with our communication technologies is grounded in history.
He also engages critically with metaphysical theories that he does not ultimately adopt.
More recently, feminist phenomenologists have engaged critically with Beauvoir's ground-breaking work, and, in so doing, have extended her insights into power.
