AOD WALKTHROUGH: 26.THE VAULT OF TROPHIES
If you used the bug to obtain extra respirators in the Louvre Gallery level, now would probably be a good time to use one of them. Then you can take your time navigating this underwater section.
Swim through the tunnel around the corner to the left. To get past the spikes, aim for the top where there is no horizontal spike and then swim through when the vertical spikes retract. Beyond the first set of spikes is a 4-way intersection of passages where you'll find air up at the ceiling. The current draws you forward here, but if you want to, you can avoid the next set of spikes by taking the long way around, through the passage to the right. (The passage to the left is a dead end.) You'll also find air above the next 4-way intersection.
At this second intersection, go left (or straight if you took the long way around the spikes). This passage appears to be a dead end. The tunnel you want is down the well-lit vertical shaft on the left. Swim down the shaft. At the bottom, straighten out so Lara is facing the vertical support beam. All passages here are dead ends except the one to the right; go that way. Swim through the long tunnel with the wooden supports. At the end turn left and then right to find an air pocket in the ceiling. Climb out here and pick up bandages and an Aqua-lung. Find the aqua-lung in your inventory under Items and use it. This will give Lara an extended supply of air, making the next sequence a bit easier.
Jump back into the water. Swim down and then continue straight ahead along the tunnel, which curves around to the right and dead-ends in a brick wall. Press Action here to make Lara kick through the stones.
UNDERWATER ROOM WITH STATUES:
The flooded room beyond is lined with the statues of Lux Veritatis heroes of bygone days. If you have the Aqua Lung, you can probably complete this sequence without having to surface for air. But in case you need it, there's another bricked-up section of wall opposite the one where you broke in. Break that wall down and swim through to find another air pocket.
To open the exit in the ceiling, first scope out the large carved plaque. (Swim up to it and press Action.) You get a notebook update: "The brothers reunited see the gates thrown open." Also note the two big carved letters on the plaque: L and V. These not only stand for Lux Veritatis; they're also a clue to the puzzle. Swim around the circle behind the statues and you'll see their names carved into their bases. Find the two statues whose names begin with L and V: Limoux and Vasiley. Pull the chain in the alcove behind each one to move the corresponding statue toward the center of the room. When you've moved both statues, magical light shoots up from their swords, breaking a hole in the ceiling. If you need it, you can get air behind the bricked-up wall first. Then swim up through the hole in the ceiling.
Cut scene: Lara climbs out of the water and changes into dry clothes.
Run down the tunnel, but slow down after the drop-off. A little ways ahead, there's a pounding block trap. To get past it, back up a few steps to give Lara time to build up speed when she runs. Start running when the block comes down and sprint through to safety before it descends again.
DEEP PIT WITH FLOATING PLATFORMS:
Continue along the passage. At the cave mouth, pull the lever on the right to raise some floating platforms. Not all of these are stable, so save your game before attempting to jump across.
It is possible to get to the alcove high on the cave wall to the right; however the pick-up inside is another Aqua-lung, which you won't need during the remainder of the game. So unless you just want the thrill of discovery, you can skip it. Screenshots and instructions for reaching the alcove are here.
To get from the cave entrance to the tunnel on the other side, you'll need to figure out which blocks are solid and use them to get across. (These screenshots show the sequence.) First back away from the edge so Lara is standing at the top of the slight slope in the tunnel opening (where there's a seam between the textures). Jump to the floating platform that's third from the left in the second row of platforms. Walk to the front edge and jump from there to the large stone ledge ahead. When you approach the far side of that ledge, three new platforms rise up from below, but you can ignore those. Instead, step back so Lara can get a decent run-up. Then take a running jump over the low wall where it angles down in a V shape to land in the tunnel opening ahead. (Thanks to Luke for this tip.)
Follow the tunnel down to the library. There are 2 undead knights here. Knocking them down twice will destroy them. (The Viper at close range works well for this, but if you have health to spare, you can use hand-to-hand attacks.) Or, you can lead the knights back along the tunnel to the pit and shoot or kick them off the edge. Or, if you prefer, you can just try to avoid them.
Examining the book on the worktable updates your notebook: "Three periapts joined together burn with righteous light to confine evil."
In the library, pull the lever to the right of the fireplace to gain an upper-body strength upgrade and open a secret compartment behind one of the bookcases to the left. Here you'll find some bandages. Once Lara is strong enough, pull the chain to the left of the tapestry. This raises the picture, revealing a climbable wall.
Climb the wall up and to the right. Grab onto the horizontal crevice, traverse around to the right and pull up onto the wooden ledge. Turn to face out over the room and jump straight up to grab the metal grating. Traverse out to the center of the room and drop onto the grating ledge. Turn left, grab the overhead grating again and traverse out toward the chandelier. At the end of the beam, drop onto the small wooden box. Lara's weight operates a mechanism, opening another secret compartment below. Safety drop to the floor and go to the compartment to get the Fifth Obscura Painting.
The mechanism you just used also extinguished the fire in the fireplace, so you can crawl through. There's a pool in the small room beyond. Jump in and swim down. Follow the underwater passage down and then around to the left. Rubble blocks the side passages at the first intersection. So continue straight ahead past the wooden support. Then, at the first real intersection, go to the right. Just above there's an air pocket. After Lara takes a few breaths, continue swimming along the tunnel as it slopes down and then turns right. At the next intersection, go to the right. (Straight and left are dead ends.) Surface in a large, round room.
Cut scene: As the floor rises, bringing Lara with it, Eckhardt, gloating from atop a high ledge, congratulates her on a job well done. He offers to trade Kurtis for the painting. Seeing no other option, Lara complies. Eckhardt orders Gunderson to release Boaz. Then he tosses the bumbling Muller down into the arena and leaves the area. While Boaz is distracted by her succulent former colleague, Kurtis gives Lara a boost up to the ledge. He tosses her the two shards and says he'll deal with Boaz.