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).
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.
Standard kanji spelling for this fixed expression.
Kana-mixed spelling; common when the kanji 極 is avoided.
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.