[na-adj] + 極まる [na-adj] + 極まりない [na-adj] + 極まる / 極まりない + [noun]
極まる and 極まりない both mean "extremely", "utterly": the quality has gone as far as it can go. They follow a な-adjective directly, with no な or だ in between, and come either at the end of the sentence or before a noun. 極まりない looks negative but means the same as 極まる – literally "has no limit".
The adjective is nearly always a critical one written in kanji: しつれい失礼, ぶれい無礼, きけん危険, めいわく迷惑, ふゆかい不愉快, むせきにん無責任. A few positive ones such as つうかい痛快 and ぜいたく贅沢 also occur.
Both forms are formal and written: editorials, complaints, speeches. Of the two, 極まりない is the one you meet more. In conversation, すごく or ほんとうに本当に before the adjective says the same thing: ほんとうに本当にしつれい失礼だ.
These go beyond the adjective + 極まる pattern.