The atmosphere can sometimes become somewhat tense.
Literal
Atmosphere [topic-は] somewhat tense thing [target-に] become [possibility-ことがある].
いささか is a literary adverb meaning 'somewhat' or 'slightly' — more formal than ちょっと or 少し. ~ことがある expresses occasional occurrence: 'there are times when X happens.' 緊張したもの turns the adjective into a noun phrase with もの.