The boat operator was always openly smoking despite the no-smoking signs.

Literal

Boat [genitive-の] operator [topic-は] no-smoking [genitive-の] sign [despite-にもかかわらず], boldly always was-smoking.

にも関わらず ('despite / in spite of') is a formal grammar pattern for concession — here, despite the no-smoking signs. 堂々と (どうどうと, 'boldly / openly / brazenly') emphasizes the shamelessness of the behavior. The progressive ~ていた marks the habitual past action. 操作者 (そうさしゃ, 'operator') is a formal compound. 禁煙の表示 ('no-smoking sign') is the specific object being defied.