Here is the walkthrough for Tomb Raider: Legacy - Secret of Babylon. You can also download it as a PDF file.
The Vault of the Book of Death
The camera showed Kraene the pedestal with the book, which she had to pick up. That was the only thing she could do, so she picked it up. When she did so, the door in the corridor behind her opened. She ran there and just when she stepped into the next corridor she realized that the guards have found her already. She turned right and got to the hall with a construction, a door in the floor and a flame. She ran around the fire and climbed up on the stony „case“ (by it´s left side).
There she turned right, jumped on the construction above the fire, then jumped on a small balcony where she quickly ran to the right (she could also run to the left, but there was a guard waiting for her), climbed up the ladder and jumped backwards.
There she pulled a lever and then got back to the hall with the construction. The door in the floor was opened now so she could go there. She entered a high room with a waterfall and an insane camera view. She ran to the corner of the room which was the closest one to the camera and climbed up on the slope, then she jumped backwards and got to the platform with the pole. She climbed up the pole and jumped backwards again, she found herself standing on the platform with the door that she could open (by the CTRL button). Anyway, she couldn´t go any further because there was another door so she returned back to the waterfall room. She jumped on the other side of the room, crawled to another room with a fountain. On the right side was another door, but she turned left and looked at the ceiling. There was a door above the vase so she jumped up and opened it.
She pushed the switch and ran to the waterfall room again, trough the door she opened before. She was on a courtyard with a rope. She jumped and grabbed the rope, then swung to the switch, jumped and activated it. Door opened below her. She climbed down (she could grab the wall covered with the plants) and picked a small medipack in the arbour. Before entering the Sacrification pit (Hall of Flames) location, she saved the game (I highly recommend it).
The Sacrification pit
She entered the hall and saw two fire ghosts fly out of the flames held by two golden statues. She ran quickly to the corridor on her right, jumped and grabbed the ceiling, moved foward while dodging the ghosts, she got to the small pool and waited there till the ghosts were drowned.
She exited the pool and run foward, to the door which she opened. She jumped on the slope, jumped again and fell on a platform (if she jumped too early, she would die in lava). On the crossroad she ran to the left, inside the room turned to the column and climbed up. She jumped on the gate, to the window and there she activated a button in the wall. Then she jumped on the second gate and to the door which opened in the wall.
Here she ran to the slope in a moment when the battering ram swung backwards, she quickly jumped on the cube between the fires before a huge boulder would crush her. If she fell on the floor with the skulls, she would die immediately.
She jumped on the column and grabbed it – she could climb it. She climbed round two corners and then climbed up, where she activated a switch. Then she climbed down and fell on the slope, jumped, turned in the air and grabbed the ledge behind her. On the stairs she jumped and activated the switch. Then went trough the door back to the waterfall room.
Again she jumped to the other side of the room, crawled to the room with the fountain and turned left, where was the door – finally open. She walked foward, opened the door and jumped over the traps. She ran into the Tomb of Souls where she opened the door in the floor and pulled the lever, then she got back to the room before the traps (the pool room). There she pulled the lever – a block appeared on the left side of the room. She climbed on the construction above the pool and walked to the waterfall – to it´s left side. She hang herself on the ledge, let go and activated the switch. She climbed back up and ran into the opened door – she was careful, because there was another guard. She got inside, ran past the battering rams and picked up the first secret.
The Cistern
She returned to the pool room and jumped into the door in the wall. She slided the slope and fell into the water – on the cross-road she swam to the left. Then, trough the maze, she got to another courtyard, to one of the fours pool.
She got out and opened the door, quickly, because two guards appeared behind her. She ran to the gardens, and, after the flyby camera, which showed her the environment, she climbed on the stony block, or, grabbed the crack in the wall and got to the alcove with a fountain. She got to the highest part of the room and pulled the lever, then ran back to the room with four pools.
She jumped into the pool on the left side and swam to the Snake hall and opened the door in the floor, pulled the lever and got back again to the courtyard. Then she walked to the gate in the middle of the courtyard and climbed on it, jumped by the platforms on the other side of the room (she was really careful about the bats).
She jumped to the window and to the room with the sunbeams. In the room with the throne she ducked and crawled to the right, to the red room. She jumped to the water and swam to the Cistern location.
She got out of the water and walked to the middle of the bridge, above her was a door in the ceiling. She jumped, opened them and climbed up. In front of her was a ladder – she climbed it and then jumped backwards, then jumped backwards once more and jumped up, grabbed the ceiling. She had to do it quickly, otherwise she´d die because the blocks were crumbling under her feet.
She climbed to the lever, pulled it and slided the slope, turned in the air so she didn´t fall on the spikes. Then she walked back to the lower room where she jumped to the door in the wall. The camera showed her the new location, so she went there. Unfortunatelly, as she ran inside, another bats appeared, so she had to run, fast.
She got to the biggest room of the cistern and ran as far as she could, turned around and saw a switch on a collumn. She jumped there, activated it and opened the door on the left side. She ran there, used another lever and picked up the second secret.
She returned to the huge room, found a climbable column and climbed up, to the terraces, and pulled the lever. Then she jumped to the water and found a hole in the wall. She swam there and got to a spiral-like corridor, exiting the water and the fortress as well, she got to the Palm courtyard.
The Palm Courtyard
She had to move quickly because there were five guards waiting for her. She ran to the far right corner of the courtyard, jumped, activated a switch and fell to the door in the floor. There she got past the traps (she just had to try many times), then looked at the ceiling. Where the God´s eye was, she could walk, where was the skull, she´d die. She walked to right corner and picked up the third secret. She got back the same way as she did get here, climbed up and got back to the closed gate.
She found another jump-switch beside the gate, activated it and ran inside, climbed on the wooden fence and got to another location, to a small square. She saw her father (Gealen) talking with the leader of the guards, then she moved the cart to the God´s eye (the coloured sqare), ran to the right corner and crawled to the hole in the wall, fell down.
In the beginning, Kraene stepped on the slope and got to the location where the flyby camera showed her where exactly she should get to. So she climbed to the first ledge and jumped to the alcove on the other side. But, because it would be quite hard to repeat it (she would fall down really often), she didn´t climb up immediatelly when she grabbed the ledge, but climbed around the corner, then climbed up, did a roll (turned 180 degree around) and jumped to the other alcove. She repeated this till she got to the hole in the wall near the ceiling.
In the maze she always turned to the left, then she finally got to the surface. When she got to the pit, she didn´t jump over it, but climbed down. She was moving quickly so the guard didn´t hurt her and in the small hole in the wall she picked up the first secret. She got back to the balcony (she climbed up the wall with green plants on it), jumped over the pit and activated the switch. Then she went to the door which was shown to her by the camera.
Seeking the crystals
Kraene was in the red corridor. She saw a crack in the wall on her left, so she grabbed it and climbed as far as she could, then climbed up to the small red room where she picked up the first crystal.
She exited the room and fell to the red hall. She jumped to the window and found herself in a huge location – the Babylon city. She went to the canyon first. She turned to the left side, saw a plant – behind it was the second crystal.
She went back to the city, passed two gates and right behind the corner in the ruins she found the third crystal.
Then she went back to the window from which she got here, but didn´t enter the red hall, she jumped at the first gate, then to the window, she walked trough the room and from the second window, she jumped to the second gate. After that she jumped to the last window and there she picked up the fourth crystal.
Now she went to the passage between the two gates and behind the column in the left wall, she found a hole. She climbed down the ladder and put the crystals to the places where they belonged. A door opened.
What happened next?
She entered the new location and was instantly attacked by the skeletons. She ran to the left, to the right, jumped over the pit, to the left and then she found a hole to which she climbed. She saw a room with three sacrophagi. She walked up the stairs and then turned to the right. She climbed up the ladder, jumped backwards and got to the upper floor of the house. Behind the corner she activated a switch and went to the balcony.
She walked to the balcony and jumped to the window in front of her. She went to the window on the left side, fell down to another balcony and picked up the second secret. Then she got back to the balcony, walked to the last window, turned around and climbed down, then climbed to the right and by the only way she could go, she got to another labyrinth. She turned to the left, then two times to the right and in the end to the left again. She found herself in an underground library. . She walked down the stairs, went to the right and climbed on the library, got to the hole in the wall in the corner of the room. Kamera showed her the environment again, so she ran still foward, turned to the right and climbed to the hole in the wall. Now she crawled to the left and then to the right.
On the bottom of the canyon
Kraene finally got to the bottom of the canyon. She jumped to the river and swam to it´s other side. She climbed out of the water and behind one rock she found the third secret. She was careful not to run into the skeletons and jumped to the river again, swam as far as she could and then climbed on the rock. She climbed as high as she could (then she climbed up the green wall) and by the platforms, she finally got to the corner of the canyon, where she found a hole in the wall. She crawled there and on the crossroad she went straight ahead. She got out the labyrinth and told the member of the Lux Veritatis what´s happened.