This walkthrough was provided by the author and is posted, along with screenshots, at:
The level commences at the exact point where 'RETURN TO THE HOLLOW MOUNTAIN' left off. In fact, it begins a moment earlier, with Lara propelled down a water tunnel toward two crocs. These will snap at her, but keep the swim button held down and she'll pass them and continue out of the tunnel, even when the current has ceased. There are two items on the floor of the water chamber (shotgun cartridges and a small med-pack). It's easiest to climb out and shoot the crocs before fetching them.
Now make your way over to the column closest to the water's edge. Do a standing jump, then step back and edge over to the right-hand side. Run / jump / grab the next column. Pull up and jump forward to the next, then jump again and grab the fourth column. Run jump and grab again. When you pull up, a movie sequence will give a clue as to where to go once the side is reached.
Turn to your right, and run / jump to the ledge. The diamond pick-up is behind you on the opposite side of the room. Climb up the two large steps, then jump diagonally onto the top of the long sloping ramp. You'll notice a ladder to climb. You can go up it if you wish (and indeed, right to the top of the room) but it will be a wasted journey without the diamond, as this unlocks a door higher up.
Set off down the long slope in 'sprint' mode. The reason for this is that a boulder thumps down behind you and rolls after you. Run to the foot of the ramp, turn right and race down the adjacent slope - the boulder still at your heels. At the foot of the second slope stop and pick up the diamond then jump into the water before the boulder reaches you. Hanging from the edge won't save you.
Retrace your steps back to the ladder, and this time you are free to climb it. Once on the upper ledge, notice the ladder on the wall behind. This is unreachable from your present ledge, and can only be attained by a series of jumps and slides around the circumference of the room. The route should be fairly obvious, but mind the skeletons on the next ledge; and be sure to get the slide / jumps timed properly.
On reaching the tall column at the end of the jump / slide sequence, take a step back diagonally and then run at normal speed off the column. You will land safely on the ledge beneath. The sloping ledge needs to be shimmied, so perform a sideways jump to reach it. Lastly, a slide / jump is required to reach the ledge with the ladder. Climb the ladder to the ledge above, then run / grab the rope. Swing / jump / grab the sloping platform. Pull up and slide / jump / grab the monkey bars. If you miss, you can backward jump onto the slope and jump / grab from there. Monkey swing to the end, then turn and jump / grab the next ledge.
Up top, a skeleton will appear one ledge away. One ledge again, beyond that, is another platform with a door set into it. Stepping on the gratings in front of you will open the door, but only for a very short time. As soon as it opens, run / jump onto the skeleton platform (hopefully avoiding it on the way) then continue with a run / jump to the door platform. Run up to the door, jump back and grab the edge, shimmy right just once, immediately pull up and run forward before the door has a chance to shut. Once inside, run forward then immediately jump back before the boulder gets you. Don't stand there too long, because the skeleton can reach you through the door.
Turn and climb up and around the inside of the room, until you reach a step. You should now be standing on one end of a T-shaped platform. A short movie will show you the exit in the roof. Run forward, and turn left down the platform to the 'key hole', jumping over the emerging skeleton en-route. Put the key in the lock, turn and run back through the opened door. Inside is a shotgun and some cartridges. You know what to do. Now climb the ladder and jump back onto the upper ledge. Walk forward and run jump. Have faith. You will land on an invisible platform. Pull up into the fresh air.
What a lovely day! Look around, and you'll see a crossbow and a med-pack. Now proceed down the path, which gets progressively narrower and darker until you slide into oblivion. Well, not really. But you'll lose some life, before you drop into a large fiery hall. The Hall of Hades! Don't touch the floor. It's clearly burning hot. You'll notice a small hallway leading off, containing another blue diamond key. To get there, you have to run / jump over several columns but (here's the catch) one has a skeleton on top, and the other is a flame burner.
Jump onto the nearest column first. Edge right back and angle yourself to the column in front of you. Perform a standing jump (when you land, the flame burner will go out) and WITHOUT STOPPING run / jump onto the next column. You should land right on its nearest edge (from your point of view) leaving just enough room to run / jump / grab the opposite ledge. You can not stand still on this burner column, as the flame only stays out for a few seconds. Now pull up and run into the small adjoining room and pick up the diamond and the explosive arrows. Arm yourself accordingly.
Back in the Hall of Hades you'll notice the change. The columns have gone, to be replaced with a floor tiled with faces. Explode the two skeletons, and jump to the nearest face. This next part is pretty tricky. As you land, you'll notice that a large flame in the distance (beneath the opposite ledge) has extinguished. However, as soon as you step off the face square, you set a timer in motion which will re-ignite the flame after 23 seconds! You therefore have to work out your route before you attempt to negotiate the room. Look up at the ceiling. The corresponding safe squares are displayed. All other face squares will burn you.
Walk close to the top left edge of your face square and angle yourself with the closest point ot the next square (that is, the one on the furthest left of the next row). Do a standing jump to get you on it. Now (and this must all be carried out as fast as possible) turn to the square in front (the left hand square of the next row) and stand / jump onto it, immediately jumping right onto the square next to it, and then standing / jump forward onto the square in front. Walk as close as you safely can to its top left corner, and stand jump onto the the closest point of the next square (the left hand square of the next row). Turn, walk foward to its top right edge and stand / jump onto the last (top) square, immediately lining yourself up to the ledge and standing / jumping to it. Hopefully, before the big flame re-ignites! Remember,...practice makes perfect.
Now place the diamond in the lock, and run through / drop down into the ante-chamber where a motorbike awaits you. Zoom off up the path ahead, jump the water and bear left at the fork ahead, jumping the water again. Ignore the next left (although it's fun to watch her die!) and drive slowly to the right, through the fence. Carefully navigate around the deep pits and turn left, immediately moving across to the right-hand edge. Zoom up the ledge directly ahead and use it's pointed crest (at an angle) to propell yourself across the chasm over to the other side. If you fall into the chasm and survive, by the way, you can't get out again. Now turn right and throttle up the steep hill. Don't worry about the skeletons; they're just seeing you off. Now bounce down into the old familiar valley, and turn right through the open gates.
Hang from the edge at the top of the drop into the Hall of Hades. As you slide down, you'll see the opening in front of you. Jump / grab / pull up.
In the dark pit to the left of the second
In the entrance / exit of the