This was taken out of my walkthrough on this site for this game. It includes the chest locations as well for this part.
Defeat the Sentries: As Prince Caspian, head to the top right corner and start smashing barrels to discover a crank looking object. Pick that up and move it to the left and put it in is spot with "B". Now, smash more barrels near the northern wall to unearth a gear. Pick it up, and go left to put it in it's place using "B". Go back to the crank, and press "B", and then rotate using the left stick to turn it, revealing stairs to climb. Go up the stairs and go over to the gate with two symbols over it. Switch to Susan, shoot the prompts with arrows, and then switch back to Caspian. Head through the door. Continue right, and head to the breakable down. Break it down and enter.
Defeat the Castle Guards: After the cutscene, switch to Caspian (so you can keep working on getting 200 kills with him), and take out the telemarines. Pick up the crank lying beside the stairs, and put it where it needs to go (follow the X on the mini map in the bottom right hand corner of screen). Run up to it, start pushing it, and watch as a bridge extends. Cross the bridge, shoot an arrow up at the icon, and go through the gate. As soon as you enter, you hear bells being rung. You have to kill the bell ringers before the timer goes empty (top middle of the screen). Run around the top to the other side to kill that bell-ringer, and then go down the steps and kill that one. Kill the other telemarines, pick up the crank on the bottom floor, and take it upstairs to put in its place. Run back downstairs, pick up the lever, and go back upstairs to put it in its place. Pull the lever, and then turn the crank to open the gate, going through afterwards. Go along the pathway, entering the next area by going up a mini spiral staircase. In this area, the bell ringer is on the bottom floor. Run around to the other side, go down the steps, and take out the bell ringer. Finish off the rest of the telemarine force in this area. Stand with the bell to the right of you, and go up the stairs right in front of you. Once to the top, go into the open gate right there. There is a chest in here, and it will cost you 2 keys (Chest 4 of 16). Around the top floor, there are 2 alcoves that have pressure pads in them. Step on run, then run step on the other. After that, go around the top floor. Two of the gates now have the arrow icons above them. As Caspian, shoot arrows at each one, and grab the crank out of one, and the gear out of the other. After putting each where they need to go, rotate the crank once. This makes the lift go up and down. Wait for the lift to come down, hop on the lift, and ride it to the top and pull the lever. This opens a new area. Go down the lift, and go left around the top floor. You will see two arrow icons for Caspian to shoot, and then one icon for Peter to grap with the grappling hook. Cross the new bridge. You know the process by now. Kill the bell ringer (he's downstairs), and kill the rest of the telemarines. On the top level, DON'T STEP ON THE PRESSURE PADS YET! Opposite the side (top level) you came in, there is a chest to open for 3 keys (Chest 5 of 16). Find the alcove with the pressure pads, and stand on one of them. The AI will stand on the other one. After this, find the new little opening on the top floor, which will give you a mini cutscene and this achievement.