。
She hurried up the stairs.
Literal
She [topic-は] hurriedly stairs [path-を] went-up [moving-away-ていった].
Two motion patterns combine. The を on 階段 marks the path being traversed, the same を used with 道を歩く ('walk along the road') and 川を渡る ('cross the river') — typical for verbs of movement. On top, 上がっていった layers ~ていく onto 上がる ('go up'), framing the upward motion as moving away from the speaker — a viewpoint particle, not a tense marker. So the speaker is at the bottom of the stairs (or downstairs), watching her ascend out of sight.