For this quest you must speak with three priests at the Sanctuary of Asklepios, located south east of where you dealt with Hippokrates. Each priest will have a task for you to complete before you can extract information from them.
Enough Is Enough
For this task you must deal with a snake problem. They have invested a local bathhouse where people go for healing. The priest strongly recommends that you do not kill the snakes. Instead, you will find a pipe in a nearby water source which you can tamper with to flood the bathouse and rid it of the snakes.
Interact with the pipe to flood the bathhouse. You can then return to the priest to complete this part of the quest.
Written In Stone
For this part of the quest you need only listen to the priest Timoxenos and persuade him to show you a stone with relevant information. Follow to where he leads in order to find the stone. When you reach the stones, speak with Timoxenos. Each time he will tell you a tale. At the third set of stones he will tell the tale of your mother, but another priest will interrupt before he can finish telling all that he knows. The priest will enquire about what you were discussing. If you want to learn more from Timoxenos and see him live, do not tell the truth to the priest. You can tell him that Timoxenos was informing you about how to cure sword wounds, and when he asks the method by which this is done, choose the 'dog licking' option. When you are done speaking with the priest, meet Timoxenos by the olive tree of Herakles. Here you will be able to learn a bit more information before you are ambushed. Defeat the ambush and this part of the quest will complete.
A Heart for a Head
For this quest you must speak with a priest who is having trouble tending to a sick girl. Before there is a chance of him telling you anything, he has instructed you to find and capture a sacred bull in the region. Head south west to find the beast. When you arrive at its location you will find that it has already been killed by bandits. You will only have to deal with one bandit which is standing by the bull. Once he is dead, all you can do is take the heart from the corpse and bring it back to the priest. You will then have to decide which of the three sick people should receive the prayers of the gods. Note that this will come down to your personal preference, and has no influence on the story to come. When you have made your decision the priest will inform you about where you can find more information on your mother, and the quest will complete.