The stare will begin with a fight - you will get attacked by shielded soldiers and undead dogs. They shouldn't pose any threat, just don't forget to switch to the Nemean Cestus.
Afterwards take a look around. In the upper left corner of the room there's a wheel. Pull it and go through the opened gate to reach a save point.
Follow the only possible path in the direction of the gate, behind which you will meet Poseidon's lover. After a short conversation go left, to the bigger room.
There you will find a couple teleports. Enter the first on the right and you will be moved onto a moving platform. From there, jump onto the ledge on the left and pull the lever found there.
By doing so you will make the bridges move and undead dogs appear. Jump down and collect experience from the two unblocked chests. What you need to do now is grab the beasts and throw them into the teleport through which you have arrived. Do this four times and then jump in yourself.
This way the platform will lower itself, which will allow you to use the last teleport.
You will find yourself in the room in which Poseidon's lover has been imprisoned a while ago. After the cutscene is over, take a look around - on the left there's an experience chest.
Poseidon's Conch Shell
On the right, in the further of the nooks you will find a Godly Possession - Poseidon's Conch Shell. There's also a Gorgon Eye hidden in the room [!!!].
Once you collect all the valuable stuff, you can return to the teleport. On the other side a fight awaits you. You will have to rescue the mistress from falling down - kill the dogs and then push her to the upper teleport.
By doing so you will initiate a fight with a new enemy. The easiest way to deal with this statue is to use the Cestus - equip it and jump right into the fight.
The enemy acts similarly to the basic statues - he's very slow and his main attack is a short distance hammer blow.
Try to stay behind his back (he turns around very slowly) and quickly attack. After you deal enough damage, a QTE mark will appear - activate it and press three basic buttons to finish the fight.
Follow the princess and you'll be attacked by shielded enemies - eliminating them is mere formality. You will have to push the lady, as she won't move otherwise.
Go along the path until you reach a locked gate - push it up and let her pass.
On the other side you will be attacked - get rid of the enemies (including the new statue type) and turn the nearby wheel once again. Kratos will automatically use the princess to hold it down, which will allow you to go through the gate by the save point.
On the other side you will have a short talk with Pandora. There's a hidden chest here, use the Head to unveil it - it contains a Phoenix Feather [!!!].
The further path leads left, outside the building.