She's very shy and can never relax at parties.

Literal

She [topic-は] very shy [and-で], parties [at-で] [topic-は] always cannot-relax.

内気で is the te-form of the na-adjective 内気 ('shy, introverted'), here linking the two clauses as 'shy, and...' パーティーでは stacks で (location) with は (topic/contrast) — the は narrows the claim specifically to party situations, implying she might be fine elsewhere. 落ち着ける is the potential of 落ち着く ('to calm down, settle in'), with 落ち着けない as its negative.