。
She went to see a movie alone.
Literal
She [topic-は] alone [by-で] movie [object-を] see [purposive-に] went.
独りで ('alone, by oneself') uses で in its manner sense. Note 独 (vs the more common 一) — both are read ひと in 独り and 一人, but 独 emphasizes 'singular, isolated,' giving 独り a slightly more deliberate or solitary feel than 一人.