No, the phrase "acutely of" is not grammatically correct.
You may be thinking of the phrase "acutely aware of," which is a common phrase and is grammatically correct. "Acutely aware of" means being highly or intensely aware of something. Example: As a doctor, I am always acutely aware of the importance of precision and accuracy in my diagnosis.
In her new book, "The Full Severity of Compassion: The Poetry of Yehuda Amichai" (Stanford), the scholar and translator Chana Kronfeld writes acutely of how Israeli (and Jewish American) appropriations of Amichai's work have often robbed it of its complicated theological allusiveness and its political radicalism.
We feel the pain more acutely of those who resemble us.
Yet more affecting, and acutely of the here and now, was the involvement of several players from Hanover's NDR Radiophilharmonie.
It's there in the very best of British game, be it grouse or snipe or venison, given the gentlest of attentions, so they taste most acutely of themselves.
Political prisoners, prisoners of conscience, were acutely of their time in the 1960s, in a world thick with dictatorship and totalitarianism - fascist dictatorships in Spain, Portugal and much of Latin America, despots aplenty in Africa, communism from East Germany through the Soviet Union to China.
Reading about those who have been wiped out by Madoff and those who were spared, I was reminded most acutely of the assassin Anton Chigurh in Cormac McCarthy's philosophic thriller, No Country for Old Men.
Most clerics err on the side of caution, acutely aware of the consequences of bad timing.
Each year, in the Netherlands, about 140,000 persons die and two third of them die non-acutely of one of these three diseases (http://statline.cbs.nl/StatWeb/publication/?VW=T&DM=SLNL&PA=71594ned).
I became sort of more acutely aware of like, "Oh that thing delights me.
He is, of course, acutely aware of how his remarks might play in the media.
Williams is acutely aware of the dangers of overclaiming.
