。
She watched the movie crying, with her eyes red from tears.
Literal
She [topic-は] cried [and-て] eyes [object-を] red made [while-ながら] movie [object-を] was-watching.
目を赤くする is the transitive 'make one's eyes red' — using 赤い in its く-adverbial form before する to derive a 'become / make' verb. Stacking it inside the ~ながら frame gives 'while making her eyes red,' i.e. while her eyes were going red from tears. The earlier 泣いて te-form chains the crying into the eye-reddening as cause-and-effect. The whole subordinate setup describes how she was watching the film — with the visible aftermath of weeping. ~ていた on 見る ('was watching') gives the whole scene a continuous, immersive feel rather than a momentary glance.