Make a huge jump towards the lowered platform. You will probably have to make a slight turn during the flight (#1). Thanks to that, Lara won't fall down. I would also recommend that you save your progress often. A few DIFFICULT jumps await you. Start off by using a nearby pipe. You have to climb up to the top. Be careful, though. The pipe will fall down in just a few seconds. You must be very fast! Make a jump towards a metal pole (#2).
That's not all! The pipes aren't very stable. You can't stay too long. Otherwise Lara would have died. I would recommend making only one swing before each jump (#1). You should be able to reach a small balcony very soon. Open the nearby door. You will find yourself in a new corridor. There are some enemy soldiers nearby. You might want to consider surprising them (#2), however this is not necessary. Be careful, though. More of them will show up very soon. Start off by killing one of the snipers (he is hiding on a balcony).
Head on to the glass door. You will find yourself in a new corridor. DON'T go right just yet. Instead, head on to the guard's room. It's located on your left. You will be able to do two things here. The central panel (#1) will allow you to take a look at the security footage. The right button, on the other hand, will activate a fire alarm (#2). Thanks to that, you will be able to see some of the lasers that are protecting the nearby corridor.
Get back to the main corridor. You could try and use dive roll moves in order to avoid the lasers, however I'd recommend an easier path. Step up to the huge ball and start pushing it towards the lasers. There's a machine gun nearby. You will concentrate its attacks on the ball (#1). You must reach the opposite end of this corridor. Wait for the gun to stop shooting! Leave the ball and head on to the left corridor. Open the new door. A short cut-scene will appear on the screen (Lara talks to Takamodo). Now you will have to deal with the remaining enemy soldiers (#2).
Head on to the RIGHT end of the huge table (starting from the door). Once again, you will have to use the grapple in order to grab the huge statue (#1). The main objective is to start swinging it. Thanks to that, the huge dragon will destroy a nearby window. Now you will have to kill two remaining soldiers (#2). You shouldn't have any problems with that. After that, use the cabinet to get to the new corridor.
Lara will have to use the elevator (#1) in order to catch her main opponent. Once you're at the top, a new cut-scene will appear on the screen (#2). You will have to take down the first boss of the game. It's a fairly easy task, however you will have to dodge most of his attacks. Your opponent is equipped with a very powerful weapon. Once you've regained control, use one of the pipes (they are located by the statues) in order to reach the upper balcony.
Thankfully, you won't have to look for any weak spots of this boss. You must only keep firing at him. Dodging his attacks is equally important. The boss will send two types of "waves" at you. In order to avoid the upper wave, make a dive roll by pressing the F key (#1). The lower wave is much easier to avoid. You will only have to make a standard jump. Keep firing at your opponent (#2). It would be best to use the machine gun. Once the ammunition has been depleted, switch back to the standard pistols.
Be careful and don't get too close to your opponent. He may try attacking you with a very powerful wave. You must avoid it at all costs. Make sure you're running all the time. You shouldn't have any problems with defeating your opponent (#1). A longer cut-scene will appear on the screen. Lara will escape from the penthouse by using the helicopter that's been provided by Nishimura (#2). Well... that's it for this level.