She held tight to my arm.

Literal

She [topic-は] my arm [to-に] firmly clung-on.

つかまる ('to grab onto, cling to, hold on to') takes its target with に, not を — a quirk that trips up learners who default to を for verbs of contact. Other に-taking verbs in this family include 当たる ('hit, run into'), 触る ('touch'), ぶつかる ('collide with'). The contrast with the active つかむ ('grab,' which takes を) is instructive: つかまる describes the grabber as the one being supported by the thing grabbed, framing the contact as dependence rather than acquisition. しっかり ('firmly') intensifies the hold.