When viewing the world map, look west from the Sanctuary of Delphi. The House of the Pythia will be highlighted on the map. Make you way there once you have dismantled or sold any items that you may have accrued while fighting the cultists.
As you approach the location of the Oracle, use Ikaros to scout the area. You will note a number of guards protecting the property; tag them and make your way towards the nearest. In order to avoid drawing too much attention to yourself, make use of assassination kills wherever possible.
In some cases you may need to whistle at guards to draw them nearer so that you can strike. In addition to guards the Pythia will have a mercenary protecting her. Save the mercenary for last as it will be impossible to kill them with one assassination kill. If the mercenary attempts to locate you before you have taken out the guards, allow them to do so and draw them away from the house, where you can deal with them separately.
If the mercenary possesses a fire weapon you must be extremely careful not to get hit. Pay close attention to their attacks and be ready to evade as they are executed. Immediately after an evasion you can retaliate with a series of heavy and light attacks until the mercenary prepares to strike again. The most effective way to deplete the health of the mercenary is by using your bow. Keep a safe distance as you inflict headshots and special ability attacks. If you do get hit by a fire attack and have no adrenaline available to heal, find cover and rest out of combat until you begin to heal and then return to the fight.
Once all the opponents guarding the Pythia are dead, walk into the house and interact with the door to trigger a cut scene. Speak with the Pythia and ask her for answers. When you are done you can return to Herodotus, who will be waiting nearby to the north west of the house, to complete the quest.
Note: If you chose to seek out the Oracle before Elpenor, you will have to complete ‘Snake in the Grass’ before you can progress any further.