He walked past the prostitute without so much as a glance.

Literal

He [topic-は] that prostitute [to-に] eyes [even-も] not-giving appearance [with-で] walking went.

目もくれない ('not even giving an eye' = 'without a glance, completely ignoring') is the idiom. 娼婦 (しょうふ, 'prostitute') is the direct term. 様子で ('with the manner of') describes his demeanor. 歩いていった uses ~ていく for walking away from the scene. The sentence captures deliberate, ostentatious indifference.