。
She's bustling around the kitchen.
Literal
She [topic-は] kitchen [at-で] restlessly is-working.
せわしなく is the adverbial form of せわしない ('restless, fidgety, in a hurry'), an i-adjective. Counterintuitively, despite the negative-looking ない ending, せわしない is the same in meaning as せわしい ('busy, restless') — the ない here is an old emphatic suffix, not a negative marker. This is one of those etymological quirks that trip up learners who try to parse it analytically. Other examples: みっともない, とんでもない — none of these are the regular negative.