Hemodialysis is life-saving therapy for end-stage renal disease; yet, 20% of hemodialysis sessions are complicated by intradialytic hypotension ("IDH"). There is a need for approaches to preventing IDH that account for their implementation contexts. Using Activity Theory, we outline the design of a digital diagnostic checklist to identify patients at risk of IDH. Checklists were chosen a priori as an outcome due to prior evidence of effectiveness. Drawing on individual interviews with 20 clinicians and three focus groups with 17 patients, we describe four activity systems within hemodialysis care. We then outline a novel design process that includes co-design activities with clinicians, and four rapid-cycle iterations that progressively incorporated activity system elements into checklist design. We contribute a new type of checklist design to HCI: one that supports diagnostic thinking rather than consistent task completion. We further broaden checklist design by including a formal role for patients in checklist completion.