。
She blinked, trying to hold back her tears.
Literal
[topic-は] blink-doing tears [object-を] stop-[try-to-ようとした].
まばたきして is the te-form of まばたきする ('to blink'), used here as a sequential connector — 'blinking, [then tried to stop tears].' まばたき itself is a noun (the act of blinking), made into a verb with する. 涙を止める ('stop tears') with ~ようとする ('try to') gives 'tried to stop the tears.' The whole sentence captures a poignant micro-moment: the act of blinking deliberately to suppress crying. This kind of physical detail of suppressed emotion is a recurring motif in Japanese narrative writing — Japanese fiction often emphasizes the body's resistance to emotion rather than its expression.