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She had to use her dictionary many times.
Literal
She [topic-は] many-times own [of-の] dictionary [object-を] use must-do.
~なければならない is the standard 'must, have to' obligation pattern, built from a negative conditional + a 'won't do' tail: literally 'if (one does) not V, (it) won't do.' The past form ~なければならなかった means 'had to V (and presumably did so).' 自分の辞書 ('one's own dictionary') is the kind of phrase that fits naturally in language-learning or research contexts, where the dictionary is a constant companion. 何回も intensifies — many times over.