。
She was very busy.
Literal
She [topic-は] very was-busy.
大変 here is the adverbial intensifier 'very, extremely' — homonymous with the noun/na-adjective 大変 'serious / difficult' (as in 大変ですね 'that's tough'). Context distinguishes them: directly before another adjective or verb, 大変 is the intensifier; standing alone or with な, it's the descriptor. 忙しい is a regular i-adjective ('busy'), here in plain past form 忙しかった.