The Earthen Peak isn't the longest section in the game by a long shot, but there are some annoying enemies and a booby-trapped chest to watch out for as you make your way through it. Follow our guide to clearing the area if you want to avoid any nasty surprises.
Earthen Peak guide
As soon as you arrive in Earthen Peak, run as fast as you can upstairs so as to avoid the poisonous enemy lurking in the alcove on your left. Kill the enemy you find at the top of the stairs, then finish off the one in the alcove in the middle of the stairs. Head back up, kill the trio of enemies you come to, then jump down into the alcove below to grab the Skeptic's Spice.
Now make your way back upstairs and jump down onto the platform below you. There's a poisonous creature down here that you'll need to kill, before you make your way through the door over on your left. Keep a close eye out for the lever on the floor around here - if you step on it, you'll take a flurry of arrows to the head. There's a pair of enemies to deal with on the other side of that door too.
As you approach the end of the next corridor, you'll see another enemy hiding in the alcove on your left. Kill it, then loot the Titanite Shards and the Soul of a Nameless Soldier from the right-hand alcove. Go to the very end of the hallway and you'll be able to open up a coffer to loot 15 Heavy Bolts and a Heavy Crossbow +3.
"If you must loot the chest inside, just be aware that it only contains a Torch, and it's booby-trapped with poison."
Go back out until you're on the ledge, and then leap forward to get onto the stairs on your left. Go into the next room along, then climb up the ladder on your right. Now go back around and head upstairs until you're back on the platform you found before jumping off it earlier.
Take the stairs to your right until you come to a mist-covered door. Take a left into a room containing a pack of enemies and kill them all. If you must loot the chest inside, just be aware that it only contains a Torch, and it's booby-trapped with poison. It's entirely your call whether to open it or not.
When you've made your decision, head back towards that misty door, then walk through it to begin the battle against the Covetous Demon.