After getting out, continue to climb until a cutscene will play and the fight will begin.
This is your first serious battle and the enemy is Poseidon. In the first phase, you have to get rid of two tentacles, stuck in the arena on the left and right side. In order to do that, attack them and dodge the enemy's attacks.
Poseidon will try to get rid of you in two ways: the first one is attacking with electricity (he'll charge up the area below you and launch the attack - avoid it by running away from the marked spot before the explosion) and the second is hitting with the tentacles behind him (before he performs this attack, Poseidon will lean backwards and give you a warning, giving you time to dodge).
After unhooking both tentacles, the camera will change position [RS] and you will have to jump onto Gaia's hand - during the jump you'll have to press R1.
This time you'll reach another fight arena. This one is definitely the hardest one, because of the limited space. Poseidon will be staying in one place for the whole time. Attack him from the front (there's a possibility to climb up the vine wall to his head, but don't do this until a QTE appears).
Your enemy will attack using three moves: a normal punch (when you're nearby), sticking his trident into the ground and electrocuting the area (it lasts quite long, so the special attack won't save you from losing health) and by a three-hit trident combo (it can hit three times at any spot on the arena).
Avoid his attacks with the right analog stick and approach him only when he's not preparing any attack.
Once you deal enough damage, a QTE symbol will appear above his head. Approach it by climbing the vine wall [RS] and start the sequence. During the QTE you will have to press two out of the basic buttons, then quickly tap Circle and press one more basic button.
After the QTE, the last phase of the battle will begin. Once more you'll have to unhook two tentacles on the both sides of the arena. The tactic you should follow and the enemy's behaviour are the same as before.
Once you manage to it, you'll have to pull off three jumps connected by swinging with R1. Remember to press the given basic button before landing.
This ways you have defeated Poseidon. Now all that's left is finishing him off. Start the QTE, press four basic buttons, quickly tap circle and in the end, press L3 and R3 (analog sticks) together.
After the cutscene, you'll once more find yourself in front of the Ares' tomb entrance. However this time you're not going inside. Save your game and jump onto Gaia's hand. Eventually you'll end up at the River Styx.