expression, adverb
in the strongest terms; scathingly; to the skies
Fixed adverbial phrase used with verbs of speaking, criticizing, or praising to mean using extreme language. Often appears as 口を極めて褒める (praise lavishly) or 口を極めて罵る (curse vehemently).
上司は口を極めて彼の失敗を非難した。
The boss criticized his mistake in the strongest possible terms.
評論家はその映画を口を極めて褒め称えた。
The critic praised the movie to the skies.
口を揃えて means 'in unison' or 'with one voice', focusing on agreement among speakers, while 口を極めて emphasizes the intensity or extremity of the words used.
From 口 (mouth) + を + 極める (to carry to extremes, to go to the limit). The phrase literally means 'to push one's mouth to the extreme', i.e., to use the most extreme language possible.