Legal term detection is an important task in Natural Language Processing (NLP) for the legal domain, serving as a foundational step for applications such as named entity recognition, information retrieval, question answering, and automated legal text analysis. Despite its importance, this task faces significant challenges in a low-resource and linguistically complex language like Vietnamese. The limited availability of datasets and the lack of optimized language models for Vietnamese, particularly in the legal domain, combined with the complex structure and diverse layouts of legal documents, present significant challenges. This paper introduces a comprehensive approach to identifying legal terms in Vietnamese legislative texts, combining Dependency Tree-based methods and large language models (LLMs) to overcome these difficulties. We present a detailed methodology for term extraction, leveraging linguistic features such as part-of-speech tagging and dependency parsing, alongside advanced generative models under zero-shot and few-shot learning settings. Our results highlight the strengths of using Dependency Tree patterns in increasing precision and the adaptability of LLMs in recall, showcasing their complementary nature. By addressing challenges such as hallucination in LLM outputs and how to effectively extract complex terms, our work demonstrates the potential of hybrid approaches in bridging precision and adaptability in legal term detection, advancing this critical field, and serving as a strong baseline for future Vietnamese legal NLP tasks.