Continue your journey with Prima's Dark Souls 2 Guide and Walkthrough
Reward: Dragonrider Soul
The most important aspect of the battle against the Dragonrider boss is the fact that his initial attack can and will knock you off the platform to your death. Anytime the Dragonrider uses his lunging linear spear attack, it knocks you back and will knock you off the platform if you're too close to the edge. If you're not around the middle of the area, chances are you will be knocked off if you get hit by this attack.
There are two main attacks the Dragonrider uses. The first is the lunge attack, with the other being one or two horizontal sweeping attacks. The horizontal attacks do not inflict as much damage as the linear attack, but the Dragonrider will use two back-to-back, in which case the damage adds up.
The best course of action to quickly dispatch the Dragonrider is to stay glued to his back. No matter which direction the Dragonrider moves, ALWAYS stay on his back. If you're directly behind the Dragonrider, none of his attacks will make contact. Between attacks and your movement to stay behind the Dragonrider, use between one and four attacks depending on the speed of your weapon.
To inflict the most damage, use magic-based attacks. This includes weapons imbued with magic properties, either temporary or permanent. Normal weapons will work, but it will take longer to bring down the Dragonrider.
With the boss defeated, head through the doorway opposite where the mist was located, then continue up the stairs. Light the bonfire at the top, then speak with Licia to the right if you wish to use Miracles (essentially healing spells).
Continue across the room, down the stairs and through the next doorway. Head down the winding staircase, then walk around the bottom of the stairwell to find a Monastery Charm. Go through the doorway to find two more enemies in the next room (which can be avoided). If you continue straight, you reach a dead end with several items that include the following: a Human Effigy, a Dark Troches, the Soul of a Proud Knight and an Old Knight Halberd.
Collect the items if you wish (you can still avoid attacks from the enemies fairly easily), then head through the doorway in the room you just passed and down the stairs ahead. Several more enemies await in the next area, but continue straight through the doorway, then to the right and down the hall. Get in the lift and step on the weight in the middle to move down to the floor below. Head through the next doorway, through the water and into the hole in the wall at the end.
Make your way through the rocky area and light the bonfire at the end. Speak with Lucatiel near the bonfire, then go through the cave and into No-Man's Wharf.