Exit the elevator shaft, and you'll find three Crystal Golems. You don't have to fight them now, but if you choose to, retreat back into elevator shaft as they gang up on you because they can't follow you in.
When defeated, walk to the end of the bridge and pillage three corpses for Azal's Staff x 1, Radiant Lifegem x 4 and Cracked Red Eye Orb x 3.
Turn back, head past the elevator shaft and and ascend the snow covered pathway, where you'll find another Crystal Golem to fight. Keep heading up, and you'll have two more Crystal Porcupines to fight. Luckily, you can lure them to a precipice and take them down in relative safety before they get their roll on.
Make your way up, turn the corner around the building and you'll have to more Crystal Golems to fight. If they charge together, back down the hill to create some distance and separation. Charge past claim high ground, and take them down.
Head back up the path where they came from and toward the corpse hanging off the cliff. Beware of a Crystal Porcupine just out of sight beyond the building, who's ready to attack and counting on you paying too much attention to the corpse and not enough to your surroundings. Take him down and pillage the corpse for Vine Balm x 3.
Walk around the building and face a Rampart Golem with a lance and a shield. Wait for him to make his moves and backstab him to death.
Walk past where he once was, walk to the left of the staircase and attack the large snowball you see on your left. It will roll down the hill, kill the three Crystal Golems standing on the bridge (if you haven't already) and lodge itself in the bridge making it crossable now.
Turn around, head up the stairs, open the gates and approach the warrior sitting in the chair there. Interact with him, and the game will inform you that "A knight of Eleum Loyce seeks the Chaos," which will help you with the final boss fight.
If you didn't kill the three Crystal Golems on the bridge, head back down the hill and pillage the corpses on the bridge.
Walk over the bridge, which you can do thanks to the snowball, enter the building on your right and make your way to the Abandoned Dwelling bonfire, which is the closest to you. Or use an item to return to a bonfire and warp to the last bonfire you were at. Ether way, when you get to a bonfire, warp to the Inner Wall bonfire from there.