In fine-grained opinion mining, the task of aspect extraction involves the identification of explicit product features in customer reviews. This task has been widely studied in some major languages, e.g., English, but was seldom addressed in other minor languages due to the lack of annotated corpus. To solve it, we develop a novel deep model to transfer knowledge from a source language with labeled training data to a target language without any annotations. Different from cross-lingual sentiment classification, aspect extraction across languages requires more fine-grained adaptation. To this end, we utilize transition-based mechanism that reads a word each time and forms a series of configurations that represent the status of the whole sentence. We represent each configuration as a continuous feature vector and align these representations from different languages into a shared space through an adversarial network. In addition, syntactic structures are also integrated into the deep model to achieve more syntactically-sensitive adaptations. The proposed method is end-to-end and achieves state-of-the-art performance on English, French and Spanish restaurant review datasets.