Multiple previous studies have reported suboptimal performance of LLMs in biomedical text mining. By analyzing failure patterns in these evaluations, we identified three primary challenges for LLMs in biomedical corpora: (1) LLMs fail to learn implicit dataset-specific nuances from supervised data, (2) The common formatting requirements of discriminative tasks limit the reasoning capabilities of LLMs particularly for LLMs that lack test-time compute, and (3) LLMs struggle to adhere to annotation guidelines and match exact schemas, which hinders their ability to understand detailed annotation requirements which is essential in biomedical annotation workflow. We experimented with prompt engineering techniques targeted to the above issues, and developed a pipeline that dynamically extracts instructions from annotation guidelines. Our results show that frontier LLMs can approach or surpass the performance of SOTA BERT-based models with minimal reliance on manually annotated data and without fine-tuning. Furthermore, we performed model distillation on a closed-source LLM, demonstrating that a BERT model trained exclusively on synthetic data annotated by LLMs can also achieve a practical performance. Based on these findings, we explored the feasibility of partially replacing manual annotation with LLMs in production scenarios for biomedical text mining.