Sixth Generation (6G) wireless networks, which are expected to be deployed in the 2030s, have already created great excitement in academia and the private sector with their extremely high communication speed and low latency rates. However, despite the ultra-low latency, high throughput, and AI-assisted orchestration capabilities they promise, they are vulnerable to stealthy and long-term Advanced Persistent Threats (APTs). Large Language Models (LLMs) stand out as an ideal candidate to fill this gap with their high success in semantic reasoning and threat intelligence. In this paper, we present a comprehensive systematic review and taxonomy study for LLM-assisted APT detection in 6G networks. We address five research questions, namely, semantic merging of fragmented logs, encrypted traffic analysis, edge distribution constraints, dataset/modeling techniques, and reproducibility trends, by leveraging most recent studies on the intersection of LLMs, APTs, and 6G wireless networks. We identify open challenges such as explainability gaps, data scarcity, edge hardware limitations, and the need for real-time slicing-aware adaptation by presenting various taxonomies such as granularity, deployment models, and kill chain stages. We then conclude the paper by providing several research gaps in 6G infrastructures for future researchers. To the best of our knowledge, this paper is the first comprehensive systematic review and classification study on LLM-based APT detection in 6G networks.