Once outside, go to the right to find a Red Orb Chest. Go to your left and grab the grapple point and then the next to slide down a wall, where you'll need to grab another grapple point. You'll eventually land on some beams that you have to climb, which will lead you to a grapple point that lets you smash through the wall.
As soon as you smash through it, grab the grapple point and begin climbing to a wooden platform. Climb the ladder and then the rock wall. There will be another two grapple points here, then you'll find two Red Orb Chests to the right after ascending a ladder. Go to your left and jump from platform to platform, where you'll fall through the third one and have to grapple to the next area.
Pick up the hammer if you want, as you'll be doing battle against a Satyr and two Satyr Generals. After the battle is over, there's a ledge on the left side of the screen that you can jump to that has a Phoenix Feather, Gorgon Eye and two Red Orb Chests. Go through the opening and navigate the narrow passages, pushing the things blocking your way. After the second one, you'll arrive at The Furnace.
