Once you've reached your destination, head on to the central part of the platform. As you've probably suspected, you will have to push a large ball (#1). Thanks to that, you will be able to complete second part of the puzzle. Now you must get back to the lowest level. I would recommend choosing the same way. Lara will make a larger jump at some point. Don't worry about that. She won't get hurt. Head on to the newly acquired ball. You will have to start pushing it. Place the ball on the LEFT button (#2).
There's only one ball left. You will find it on a pillar that's located near the huge corridor with the traps. You will have to use your grapple. Target it at the glowing object (#1). After that, start pulling the construction towards Lara. The whole pillar will crash down, so you must avoid it at all costs. Head on to the sphere and start pushing it. You will have to place it on a central button. You will be rewarded with a new cut-scene (#2).
The first movie will involve the puzzle itself, the second one will explain more things about the whole tomb. Use one of the nearby ladders. Start climbing up to the top floor (#1). Once you're there, a new cut-scene will appear on the screen (#2). It would be best to listen closely what Lara and her associates have to say. You will find out more about Lara's new trip, however your main problem right now will be to leave the temple safely. You will also be informed that some mercenaries have arrived in the area. You will have to take care of them along the way.
Don't use the ladder, because you will have to stay on the upper floors of the cavern. There are some quite challenging jumps ahead of you. Turn right and make a jump towards a nearby ledge (#1). Climb up to the main platform. You will have to make a jump towards a new ladder. Start climbing up to the top area of the platform. Now you will have to reach the opposite platform (#2). You will find yourself by a huge wall. Make a single jump and start moving towards the left edge of the screen.
There are some gaps along the way, so you must be very careful (#1). Each jump should be well executed. Nevertheless, you shouldn't have any major problems with these type of actions. Once you've reached the opposite end, climb down (use the F key). The most difficult jump involves grabbing a nearby ladder (#2). Turn right and start swinging in order to reach a huge pillar.
You should be able to hear some of your opponents in just a moment. Thankfully, they don't suspect any kinds of attacks, so you will be able to surprise them. Head on to the next pillar. Get down to the lower platform and take care of the enemy soldiers (#1). I have to warn you, though. There are more of them nearby. One of the soldiers will be standing in a large corridor (#2). Use the ropes in order to get through to the next area. Keep moving forward.
Once you've reached a large cavern, take care of the remaining enemy soldiers. Don't forget to pick up medkits and ammunition along the way. Use the rope. Start climbing towards the top of it. Turn around. You may start swinging now. You will have to reach a small passage (#1). There aren't any new units nearby. Use the ladder (#2) to get to the upper floor.
You will come across several new platforms along the way. Use the next rope in order to leave the underground complex. Once you're there, make a single jump towards a new platform (#1). Start running towards the dig site. Be careful, though. There are some new enemies here. It would be wise to use grenades and machine guns during these fights (#2). Bear in mind that some of the enemies will try throwing grenades at you. I would recommend that you make a lot of jumps. You might also consider aiming at the highlighted objects.
One of the soldiers will try to kill Anaya. You have to protect her at all costs. Anaya is located near the Jeep, on the top floor (#1). Kill the soldier in order to rescue her. A new cut-scene will appear on your screen (#2). After that, this mission will come to an end.