。
She was tied up with that work for a whole day.
Literal
[topic-は] full 1-day that work [by-に] was-pursued.
まる一日 ('a whole/full day') uses まる as a prefix meaning 'whole, entire, full' — まる一年 ('a full year'), まる三時間 ('three full hours'). 追われる is the passive of 追う ('pursue, chase') — 'be pursued (by)' — used metaphorically for being besieged or overwhelmed by tasks/demands. に marks the agent (the work). 仕事に追われる ('be tied up with work, swamped') is a stock phrase for the busy professional life that's deeply familiar in Japan, where long hours and 'work death' (過労死) have entered the international vocabulary.