。
She looked at me with pleading eyes.
Literal
She [topic-は] appealing [like-ような] eyes [with-で] me [object-を] looked-at.
訴えるような目 creates a vivid simile — eyes 'as if appealing.' The verb 訴える (to appeal, to plead) is used figuratively, evoking an unspoken plea communicated through gaze alone. ような turns the verb into an adjectival modifier for 目, and the particle で marks the eyes as the instrument or manner of looking. This kind of body-language description is a staple of Japanese narrative prose.