Step 1: Vāgbhaṭṭa (A).
Vāgbhaṭṭa is the author of the famous work Aṣṭāṅgahṛdaya, which is a foundational text in Ayurveda. Hence A - II.
Step 2: Hemadrī (B).
Hemadrī composed Lakṣaṇaprakāśa, a work dealing with symptoms and diagnostics. Hence B - III.
Step 3: Cyavana (C).
Cyavana is associated with the text Jīvanānam, emphasizing rejuvenation and therapy. Hence C - IV.
Step 4: Bharadvāja (D).
Bharadvāja is credited with the tradition of Agadatantra (toxicology). Hence D - I.
Step 5: Conclusion.
Thus, the correct matching is: A - II, B - III, C - IV, D - I.