Software development in critical healthcare domains presents unique challenges due to the non-deterministic nature of Artificial Intelligence (AI). Traditional agile frameworks often face friction when aligning the exploratory cycles of model training with fixed sprint cadences. This paper presents a case study on the development of a mobile application for diabetes patient support, powered by a specialized Large Language Model (LLM). The project adapted Scrum ceremonies to manage the full AI lifecycle, from corpus preparation to clinical validation. We identify four key challenges, specifically the insufficiency of automated metrics (e.g., BERTScore) to ensure medical safety and the limitations of standard “Definition of Done” (DoD) in experimental contexts. As a solution, we implement “hybrid sprints” incorporating “question stories” and multi-level acceptance criteria that prioritize clinical expert validation over technical scores. The results demonstrate that while standard agile methods provide a foundation, they require pragmatic decoupling of data and model lifecycles to ensure safety-critical value delivery.