I almost got taken in by some dealer's sweet talk and would have lost a bundle.

Literal

Almost certain-dealer [genitive-の] sweet-talk [to-に] be-deceived-and big-loss do was-at-the-point-of.

A narrow-escape anecdote. あやうく ('nearly,' 'narrowly,' 'almost') is an adverb meaning 'by a close call' — it signals that the speaker nearly suffered a bad outcome but didn't. Paired with ~ところでした ('was just about to X,' 'was on the verge of X'), which is the past form of ~ところだ expressing 'was on the point of (doing/happening).' Together: 'I was almost X-ing / I barely avoided X.' 某業者 ('a certain dealer') uses 某 (ぼう, 'a certain'), an archaic/formal indefinite pronoun for people or organizations whose identity the speaker declines to name. 甘言 ('sweet talk,' 'honeyed words') is a register-marked compound for flattery or seductive promises — more literary than 甘い言葉.