Start swinging on the pole. Now you will have to make a double jump in order to use the grapple (#1). The next action will require you to reach a second pole (#2). If you positioned it correctly, you will be able to use it at this moment. The pole will turn left.
Head on to a nearby ledge. You will have to start climbing upwards. There are some narrow ledges where (#1). You shouldn't have any problems with the upcoming jumps. One of them will lead you straight to a big chain (#2). Keep moving upwards. Once you're at the top, make a jump towards the roof of the main tomb.
Start moving forward. You should be heading to a central part of the roof. You'll find a rope here. You will have to use it. This time you must reach the main tomb. Start off by sliding down (#1). A longer cut-scene will appear on your screen shortly (#2). Lara will finally get inside King Arthur's Tomb. Before retrieving the new artifact, you will have to solve a puzzle.
I have to warn you. This puzzle is not too obvious, so it would be best if you followed my steps. Head on to one of the smaller tombs. They are located on your left. A short cut-scene should appear on your screen (#1). Once it has ended, start pulling a movable object towards Lara (#2). You will have to leave it near a large pillar that's located in the central part of this tomb.
The following actions must be done quickly. Thankfully, even if you fail at some point, you will be able to repeat these actions without any problems. Start off by standing near the main tomb. Turn around and use the grapple in order to grab the chandelier. You will have to pull the rope in order to make it start swinging. Now start RUNNING towards the left pillar (#2). You must climb on top of it (#2). Use the movable object to help you reach it.
Now you will have to make a QUICK jump towards the nearby rope. You shouldn't have any problems locating it (#1). As a result, you will raise the huge bell. If you're lucky, it'll crash with the swinging chandelier. As a result, a new cut-scene should appear on your screen. Lara will finally acquire a new part of the artifact (#2). Sadly, it won't be given to you without a price...
As you've probably noticed by now, the main gate is opened (#1). You have to go there now, because it's the only way out of the tomb. A new cut-scene will appear on the screen. Lara is going to be attacked by a huge creature (#2). You will have to get rid of it now.
You should know that you won't be able to wound the boss simply by using your pistols or a machine gun. It won't do any good. I would recommend that you have the Accurate Aim mode turned on. Start shooting at one of the highlighted objects (#1). If you're lucky, the creature will leave you alone. Wait for the moment it turns toward the highlighted object (#2).
Now you must QUICKLY holster your weapons. Use the grapple. You will have to be aiming at the highlighted mechanism (#1). If you're fast enough, you should be able to pull down a metal cage (#2). The object will hit the boss, wounding it seriously. You will have to repeat this combination of moves with the remaining three mechanisms. If you're lucky, you shouldn't lose any health here. The only thing you have to remember is to ignore the creature and concentrate only on both mechanisms (the bell and the anchor).