The notes that Hippokrates needs are in the possession of a chief physician who can be found at the nearby Fort Tiryns. The fort is located south west of the Sanctuary of Hera. When you reach the fort you should use Ikaros to scout and identify the amount of guards that you will have to contend with. From here you can choose to slaughter everyone in the fort in order to retrieve the notes, but since Hippokrates pleaded against this there is a more direct route to the notes with minimal bloodshed. Once you have identified any threats with Ikaros, approach the fort from the centre of the western wall.
Note: If you have a tamed animal companion, be sure to dismiss it before you go any further, lest it obstruct your attempt to infiltrate the fort in stealth.
Approach the western wall while crouched. Take note of the patrolling guards on the walls and wait for them to walk out of your line of sight before ascending the walls. Once atop the fort walls you will find a gap from which you can jump down to the room where Dimas, the fort doctor, is working.
When you encounter Dimas he will inform you that Hippokrates’ notes were burnt in a recent fire. You will therefore have to persuade Dimas to meet Hippokrates himself. You can do this either by suggestion of force (this will result in the death of Dimas’ patient), by waiting for Dimas to heal his patient before he comes with you (this will result in the death of Hippokrates’ patient), or by bribing Dimas to come with you once he is done with his current patient (this will cost 10,000 drachmae, but you will have a chance to refuse if you initially chose it). While costly, bribing Dimas is the only way to ensure that both patients survive.
Whatever you choose, return to Hippokrates and inform him of what you have done. He will reveal some information about your mother and the quest will complete.