AI-powered recruitment tools are increasingly adopted in personnel selection, yet they struggle to capture the requisition (req)-specific personal competencies (PCs) that distinguish successful candidates beyond job categories. We propose a large language model (LLM)-based approach to identify and prioritize req-specific PCs from reqs. Our approach integrates dynamic few-shot prompting, reflection-based self-improvement, similarity-based filtering, and multi-stage validation. Applied to a dataset of Program Manager reqs, our approach correctly identifies the highest-priority req-specific PCs with an average accuracy of 0.76, approaching human expert inter-rater reliability, and maintains a low out-of-scope rate of 0.07.