。
She sat perfectly still so as not to wake the baby.
Literal
She [topic-は] baby [object-を] wake-not [so as to-ように] motionlessly was-sitting.
じっと is a 擬態語 (state mimetic) meaning 'motionlessly' or 'fixedly' — it conveys deliberate stillness, holding one's body or gaze steady. Combined with 座っていた ('was sitting'), it paints a vivid picture of someone frozen in place to avoid disturbing the baby. The ように pattern marks the negative purpose: 'so as not to wake.'