。
She seemed as if she'd met me somewhere before.
Literal
She [topic-は] somewhere [at-で] me [to-に] met experience [subject-が] exists [seemed-ようだった].
~たことがある is the standard 'have done X before' frame, where こと nominalizes the past clause and ある states its existence: 'an instance of past meeting exists.' Wrapping the whole thing in ~ようだった ('seemed') casts the experience as inferred rather than stated — perhaps from her hesitation, gaze, or small reaction. A quietly cinematic shape used in narrative.