。
She drove out a big snake with a plastic toy bat.
Literal
She [topic-は] plastic's toy's bat [with-で] big snake [object-を] beat-out.
たたき出す is a productive compound verb (たたく 'beat, hit' + 出す 'put out') meaning 'to beat out, drive out by hitting.' The ~出す suffix on motion verbs creates 'do X out' meanings: 追い出す ('chase out'), 蹴り出す ('kick out'). The instrumental で stacks here: a plastic + toy + bat, all genitive-linked with の. The image is gleefully absurd — using a child's toy to deal with a real snake.