Stand on the platform before the main entrance to the temple and press L1 when the statue unleashes its rays at you. Get inside and defeat all the enemies there. Go down the ladder. A difficult fight awaits you there - lot of enemies at one place. If you run low on health, there's a chest with green orbs on the right side of the room. Go further to see a short scene with a soldier running away with some piece of equipment.
Use the turnstile to lower the elevator. Stop it half-way, then go to the opposite mechanism and use the stones to get back up. Defeat the monster and use a save point here if you want to. Go back a few steps and use the corridor to go left. Climb the wall and go along the ceiling to the other side, avoiding the spinning blades. Use the turnstile and quickly run through the tunnel to the right. Use the door to open the gate. If you're not fast enough, you'll be crushed. Jump down to the newly opened hall. You'll now fight Euryale.
In the first phase of the battle you have to use the Golden Fleece whenever Euryale tries to petrify you. If you let her turn you into stone and don't free yourself fast enough (by shaking the left analog stick), you'll surely die on the spot. You can avoid her tail attacks by jumping, rolling around is not that useful in this battle. Each time you succeed in reflecting Euryale's projectile, she'll drop some blue orbs for you. Use them to deal damage through Chronos Rage.
When you deal enough damage to this disgusting creature, she will climb one of the pillars in the back of the screen. In order to attack her, you'll have to use magic moves (or get close enough, but magic is far better here). Her attacks are easy to reflect as long as you feel good about using Golden Fleece. In order to get to the final phase, you have to knock down both pillars by pressing fatality button when prompted.
The final phase itself is very similar to the first one. The only difference is that Euryale is a little faster and more aggressive. Use a lot of magical attacks, some Rage of the Titans wouldn't hurt either. You finish the battle by executing a standard fatality.
When you defeat Euryale, you will collect her head. It will enable you to turn your enemies into stone. You select it by pressing "up" on the d-pad, and then pressing L2 and holding . The idea is to smash the petrified enemies to pieces before they regain consciousness.
Try out your new power on few enemies that attack you, and a passage will be opened for you. Use a save point if you want to and go to the next hall. Use the turnstile in the middle to expand a hook. Now use the lever on the right, slow down time (L1+R1) and swim under the raised grate. Use the underwater lever to keep the grate open. Use another turnstile and dive again to find another lever. Two new grates will open - use quick swimming (holding and letting go R1) to get to the other side before they close again. Use the third turnstile (there's a stone door near it, smash it to get a Gorgon Eye).
Smash through the wooden, underwater door (tap R1). Use the final turnstile and the final lever at the back of the screen, then go to the right.
Before you reach the ladder, check out the room just before it, on the right. Use the turnstile (whoops) near the statue and you will be attacked by a bunch of enemies. When you defeat them, use the turnstile once more. Slow down time (L1+R1) and run up the ladder, then quickly use your blades to jump through all the hooks you've lowered. Phew, now that was a long one!
Use the lever. A bunch of dogs will enter the elevator. Defeat them all. When the elevator reaches the top level, you will have to quickly tap O in order to save yourself. You have to repeat it 4 times before the door finally opens.
Go along the corridor, defeat the imps and go through the planks. Grab the edge of the stone to the right and get to the other side. Another Titan Minotaur awaits you. It seems to be a little tougher than the previous one, but is still pretty easy. The technique is the same: jump near it - throw some punches - jump away when it's about to attack. When you defeat it, go further, along the corridor and up the stairs. Use the lever to find yourself back in Destiny's Atrium.