。
She has completely forgotten that she ever met me.
Literal
She [topic-は] me [to-に] met fact [object-を] forget [completely-てしまって] is.
A three-layered verb phrase: 忘れる ('forget') + ~てしまう ('end up / completely') + ~ている ('present-perfect state'), giving 忘れてしまっている — 'has ended up in a state of having forgotten.' The ~てしまう adds the slightly regretful or final flavor: not just 'forgot,' but 'forgot completely / forgot, unfortunately.' The ~ている then shifts the time-frame from 'forgot' (past event) to 'is in a state of having forgotten' (current state). 私に会ったこと is the nominalized 'the act of meeting me' — こと turns the verb phrase into a noun.