This way you will get inside the Titan. Nothing can hurt you here, apart from falling down a pit. Move forward, slip through two walls and you'll reach a wall with vines. Climb up and you'll reach...
... Gaia's Heart. You'll visit this place once more, but I won't tell you anything for now.
It this room you can find the first Godly Possession - Zeus' Eagle. In order to get it, climb up the wall on the right [LS] (don't move the rock block) to its top and get on the ledge [RS]. That's where you'll find the item you're searching for.
Now you can jump down and move the block from the right wall to the gap on the left (previously turning it by 180 degrees). This way you'll unlock a vine path forward.
In order to reach the next ledge, you'll have to jump over a gap. During the jump itself you'll have to press R1 in order to swing.
On the other side some minor enemies will attack you - you can eliminate them using your new ability, the Battering Ram (unavailable in the previous games). The tutorial will tell you how to perform it.
At the end of the path there's another vine wall, use it to jump over to the next ledge (press R1 once more to swing).
In order to get to the surface, jump onto the vine wall and climb up, while eliminating enemies on your way.