The destroyed statue will lead you to Hades' throne room. As soon as you get there a conversation will start, and afterwards a very demanding fight will begin. At the very beginning Hades will try to rip out your soul. Fight back by quickly pressing L1 and R1. Later on the Underworld god can use some similar attacks, but the process of saving Kratos will be the same.
After you defend against the first attack, the main battle will begin. It consists of 5 phases, with the beginning 3 being very similar to each other, apart from the increased aggression and some of the enemy attack.
At first be ready for Hades to attack with his claws (the purple weapon). He'll be sing short and long range attacks. Additionally if you get too close, he can damage you with a foot stamp.
Long range attacks can be divided into two types: horizontal and vertical. Dodge the vertical ones with the right stick (roll sideways). As for the horizontal, you can jump over them, however Hades sometimes hits higher, so look out not to jump then.
From time to time Hades will grab the ceiling and create a shock wave. You can get damaged by the wave itself and not by staying on the ground as he hits - remember that and jump in the right moment (a second after he lands).
As you deal enough damage to the enemy, the first phase of the fight will end. You will have to launch a QTE, which consists of pressing the Circle rapidly and afterwards an intermediate phase will begin.
The intermediate phase is the key to victory in this battle, especially on higher difficulty settings. It's when you'll be getting ready for the next fight. As the QTE ends, Kratos will rip out a fragment of Hades' flesh and throw it to the opposite side of the room. You task will be to destroy it before it manages to get back to its "owner" (the flesh will be alive). Attack it with knocking back combos and be ready for your target jumping sideways to avoid getting hit.
That's not all, as demonic hands will also appear. They're very important, as you'll receive health for killing them. If you're playing on a higher difficulty setting, you should firstly take care of them, while knocking the flesh part back.
Don't worry too much if the flesh manages to return to Hades. He'll get weakened much faster. To sum up, it's more important to recover your health, taking care of the enemy comes second.
By destroying the flesh fragment you will enrage Hades, who will launch a special attack. The camera will zoom out and show the room from the top. This way you will see the floor and be able to dodge the attack more easily (on higher difficulty setting, getting hit by this attack can make surviving the next phase very difficult).
Hades will cover the whole floor with black sludge. After a couple seconds a part of the ground will cleaned up and that's where you should quickly go to. The other part of the arena will be pierced with chains. If you don't save yourself from it (use the right stick), you'll lose a lot of health.
The second phase of the fight will begin. It's pretty much the same as the first one, but Hades will be much more aggressive.
The third phase (after you go through another intermediate phase and fill up on health) bring some new attack. Hades will try to hit you with chains coming out of the ground [LS]. Keep running until he stops.
He can also summon Cerberus ghosts, always more than one. If he does, quickly jump to avoid their rush - they disappear after this attack.
After the third phase there will be no intermediate stage, the fourth one will immediately begin. During it you will be playing tug-of-war with Hades. To help yourself, hit him using either of the buttons responsible for attacks.
There's a chance you will be thrown into the Styx [RS]. Keep pressing Circle to not fall into the water.
Once a QTE mark appears above Hades' head, press Circle and then keep mashing it.
Claws of Hades
This way you will obtain the Claws of Hades. It's an alternative to the original chains. It's very fast and has a long range. I'd recommend using them on big groups of weaker enemies.
As a special attack, you can summon a monster's ghost. You'll have a wide range to choose from, you can choose one by pressing triangle in the weapon change menu.
Unfortunately it turns out that Hades is still alive. Without his armour he will undergo a mutation and his appearance will begin the fifth and last phase of the battle (fortunately it's also the easiest one).
The arena will be divided into two parts, you can move through them by doing a jump with a swing. Unfortunately you won't be able to jump constantly, as after you jump and hit the enemy in his back [RS], he will turn around and put the hooks into motion. For a moment you will have to focus on dodging the enemy attack (punches and sometimes a wave of purple energy).
By dealing enough damage, you will be able perform the last QTE (no interaction needed).This way you will rip Hades' soul, allowing you to freely travel through the Styx and the Hyperion Gate.
After the cutscene, you will have the chance to save your game. Afterwards dive into the Styx. At its bottom (before you swim with the current) you will find a Godly Possession Hades' Helm.
Swim forward, pass the god's dead body and you will reach a spot where a couple of enemies will attack you (it's a good opportunity to test out your new weapon and its special attack).Afterwards dive into the water.
At some point a locked gate will block your way. Don't worry, the lever opening it is right above the water. Pull it and unlock the path leading to the Forge.
Once there, talk to Hephaestus and head to the well-known place where you began your adventure in Hades. On your way there you will go through the round room. This time the stone statues will come to live and attack you (accompanied by undead dogs) once you try to turn the lever.
Once on open space, head to the Hyperion gate, which time will be working and will offer you its teleporting services. Jump in and head to the surface.