Head away from the bonfire near to the Last Giant, then make your way down the ladder and into the room with the lift. Go out the door here, and then use your Soldier Key on the locked door to your right. Pass through it and then go upstairs.
Kill the two guards you encounter, then carry on up the next stairway until you're at the top. Don't head into the mist here quite yet. Instead, make your way up the stairs just right of that mist, and grab the handful of Lifegems and the Soul of a Nameless Soldier from the corner.
How to kill The Pursuer
Unlike most of the boss fights in Dark Souls 2, the best approach to take against the Pursuer is to stay as far away from him as possible. Whenever he lifts his shield and charges in towards you, simply dart out of the way, and then launch your own counter-attack. Don't take more than two swipes yourself though, and only do that if your weapon speed can support it. You should only ever counter-attack when he finishes dashing, or after the boss has used his glowing blue attack, or his three-hit flurry.
If you've found yourself in a corner, and are struggling to evade the incoming damage, the best tactic is to simple dodge the first two-thirds of the three-hit combo, then slip in behind the Pursuer to avoid the final attack altogether. If that blue stabbing attack is causing you a problem, dodge to the left or the right just before it lands to get out of its range.
"You have very limited opportunities to heal up or launch your own attacks, and so the battle against the Pursuer lasts much longer than most other fights."
It's very important to exercise patience and restraint in this fight. You have very limited opportunities to heal up or launch your own attacks, and so the battle against the Pursuer lasts much longer than most other fights. If you try to hit him harder and faster than suggested in this guide, you can pretty much guarantee the Pursuer will punish you hard. Tempted to grab the crossbow in the corner? Pick it up if you find yourself nearby at any point, and assuming the Pursuer's on the opposite side of the room, but otherwise just ignore it during the fight itself.
Head to the Lost Bastille
Once you've killed the Pursuer, go through the gap in the rocks just ahead of you, then go all the way up the stairs on your right. If you interact with the bird's nest nearby, you'll be packed off to the Lost Bastille. Light the bonfire, and then make your way along the path, using the broken stone to get over the ledge. If you go around to the other side of this structure, you'll be able to loot a Large Titanite Shard and a Radiant Lifegem.
Go back around once you've finished looting and use the broken stone to get over to the balcony. Kill the enemy ahead of you, then go through the door. There's a crossbow-wielding enemy and a dog below you - take 'em out from range if you can. If you're getting all up in their faces instead, be careful of those explosive barrels nearby. Once all of the enemies are dead, go through the door and loot the Covetous Silver Serpent Ring and the Antiquated Key from the coffer.
Go back into the other room and then climb the ladder that's ahead of you and to your left. Leave the room, and then get onto the main path on the left. Carry on down this path until you come to some barrels and boxes. Roll through all of them to smash them to pieces and expose a new door in the process.
Open up that door and talk to Lucatiel on the other side of it for a Human Effigy. At this point you face a choice. You can carry on through the door and kill all the enemies you encounter - tough, but definitely doable. Alternatively, you can use one of your Homeward Bones to get back to the previous bonfire and travel to Majula. From here you can take the route that goes through Heide's Tower of Flame and No-Man's Wharf. There are no easy journeys in Dark Souls 2, but you might find this latter approach just a little easier.