She [topic-は] me [object-を] even-a-glance [without-ずに] passed-by.
ちらりとも is emphatic — ちらり ('a quick glance') + と + も ('even'): 'not even a glance.' The literary negative ~ずに ('without doing') adds a narrative feel. 通り過ぎる ('to pass by') is a compound verb combining 通る and 過ぎる.