After obtaining the 3 GOLDEN STARS, exit the ROOM WITH TWO HUGE GEARS through the east door.
Move to the edge of the opening near the climbing pole where you first entered this area. Stand to either side of the pole, and when the blade moves to the other side, run off the edge to fall safely into the passageway below.
Follow the hall to the other pole. Grab onto the pole and climb up until Lara is hanging just below the blade (i.e., 3 pulls up the pole).
When the blade moves into the front right corner, about to pass in front of Lara...
...quickly climb up once more...
...and immediately backflip off the pole to land on the ledge above. If you didn't do it on the way down, shoot the 2 vases to get a large medipack and shotgun shells.
To get past the next blade, walk to the edge, hop back once...
...and then take a standing jump to grab the pole.
Climb up three times.
Wait for the blade to move toward the front right corner, so it's about to pass in front of Lara. Then quickly climb up twice...
...and backflip to land on the ledge above.
- OR -
If you prefer, you can instead, stand at the edge of the opening.
Wait for the blade to move to the far right corner.
Then take a standing jump to grab the pole...
...and immediately backflip onto the ledge above and behind. Shoot the ceramic vase for a small medipack if you didn't get it earlier.
Next, position Lara so she's facing west or south, so there is open floor not wall behind her on the upper level. Then use either of the techniques shown above for the second blade to get past the third blade.
When you reach the top level, turn around and follow the corridor back to the MAIN HALL.