There's a welcome committee waiting for you in the first room. Nothing special, just a few undead. There's also a note on the ground.
In the second room you will have to face a riddle. Firstly go left [LS] (there's an experience chest there). You should notice a lever, which unlock the gate on the upper floor, but only for a couple seconds. In order to be able to use the passage, go right [RS] to the room with rock blocks on a cart.
Push it to the circle (while eliminating the Harpies) and block the mechanism so that it can't return to its default position. Now all that's left is to climb up using the tree, collect experience from the two chests found there and go through the gate there.
Right behind it you will be attacked by a group of enemies, including Minotaurs. They will make the fight a little harder than usual.
Kill them all and continue deeper into the Palace. You will arrive at the main hall, with a big statue of Hades in the middle. Right before it there's a book - read it and by doing so, lower the coffin with Persephone (who Kratos killed in Chains of Olympus).
This way you will lower two ladders, on the left and right side.
Before you can get to them, search the area for a couple priceless chests. Firstly head to the room on the left [LS]. There you will find a ladder. Climb it to find two experience chests and one (hidden behind a wall [RS]) containing a Phoenix Feather [!!!].
Just like before, you will find two experience chests on the right side.
Now you can solve the puzzle. Firstly head to the ladder on the left side. Climb it to find yourself in the familiar room with lever and lift. Use the moving platform and go down. This way you'll get to the place where you used rocks to block the timed mechanism. Open the gate and take the rocks with you upstairs, using the lift again. Push them near the circle and leave for now.
Return to where Persephone rests and turn crank. It's timed, so you have to be quick again. Afterwards go back to the place where you left the rocks, turn the wheel and block it.
Now you have to repeat the process with the wheel on the right side, just without the need to block it. This way you will expose the statue's torso, which will allow you to destroy it. Swing the poor deceased and make yourself a path (Kratos will automatically enter).