Following the lead of Alkibiades, you will have to sail to Korinthia to find Anthousa.
When you have docked your ship, make your way inland to where the quest marker is located in Korinth. When you reach the Porneion, look for the woman with the search icon above her head and speak with her. She will provide you with some information about Anthousa, and where to look in order to find her; atop the Akrokorinth, a nearby monolithic rock.
There you will find a temple which is being harassed by bandits. Confront the bandits and kill them (they are incredibly weak, but three more will come once you have dealt with the first three) You will then be able to speak with the worshippers for more information. When you are done speaking with them, head west down the rock to find Anthousa at the Spring of Peirene. When you speak with her she will ask you to help her before she will tell you anything. Navigate the dialogue options to complete the quest.