Across the hall where you picked up the item, there's a closed stone door. We'll open this in time. Straight down the hall is a hole in the ground. Jump over the hole, walk down the hallway and use a projectile weapon to activate the Stone Switch embedded in the wall.
Walk to the top of the staircase in front of you and shoot the Stone Switch on the far wall. Enter the door to the right of the switch and turn left to battle a poisonous soldier.
Walk toward the staircase, but don't walk down. There are two more soldiers to defeat, and you can do it without ever deploying your weapon. The soldier at the base of the staircase will see you and begin to charge. When he does, stop on the Pressure Plate at the top of the stairs, which will cause spikes to eject from the sides of the staircase and kill him. Walk down the steps, coax the other soldier up, and use the same technique to kill him.
Walk down the stairs in safety and open the three chests. The one on the right has Twinkling Titanite x 3 and Petrified Dragon Bone x 3 while the one on the left has Boltstone x 3 and Bleed stone x 3. The switch you activated atop the stairs in the hallway opened the room with the middle chest, where you'll find a Puzzling Stone Sword x 1, a bizarre glowing weapon that acts almost like a whip with its strong attack and has an S bonus to Dexterity. Now it's time to drop down the hole you jumped over before.