The objective here is to turn 4 valves on, each corresponding with the four elements whose stones you put in place. The Wind valve is to your left when you enter the room. Turn around and check the platform at the other side (should have a large pipe). Jump to it and on the other side of it should be a chain to take you to another platform. This will lead you to the Water valve.
Go back down the ladder leading to the water valve and use the chain to go back to the circle shaped platform then do a running jump to get back to the entrance (may want to hit the action button in mid- jump to make sure you make it). Go down the ladder to the left side of the entrance and down the next ladder on the other side of the platform below. There's a skeleton to fight off- use V-Packer to knock him into a lava pool. You'll find some ammo clips for the Viper on the other side of the machine here. Head up the nearby ladder and look for a chain. You'll see the Fire valve but it is blocked by bars.
Jump and grab the chain and go to the other side. Climb up the ladder and jump after the 14th step to land on a platform. Climb another ladder at the right and turn the Earth valve on top to the right. Go down the ladder and drop down near the other one. Grab the chain again and return to the circular platform with the Fire Valve at the left. You can now turn it. Once you do so, the room will be filled with slicing propellers. You have to return to the Hall of Seasons again. To easily leave this room simply hang the edge and drop down to the lower level from the Fire Valve and run to the ladder a little to the left, taking caution to avoid being hit by one propeller (run by after it passes). Go up the two ladders back to the entrance. Head up the stairs, pressing the lever on the left to open the gate on your way. Once you pass the door to the underground gallery, go right.
Jump over the next two holes. You then have to deal with spikes. You must walk in "S" to avoid them. As soon as the platform narrows, walk forward to activate all the spikes and learn how to avoid them by passing at the opposite side from where they come. The spikes come from the left, right, right, left and then right. Jump over the next hole. You will see the machine stopped, but it will move again against you as you approach it. You have an opening and there's enough time to get to it before the machine kills you. You can also collect the V-Packer Standard Cartridges if you didn't get them before. Continue to the right and jump over the next hole. The path becomes narrow after that hole, and don't stop running until you pass the entrance at the right, because a razor wheel will come from the right wall. Don't worry, because as much as you don't stop running there's no way it will kill you. At the next path use the elevator to go up. Pull the elevator chain once and turn around collect the Health Bandages and the V-Packer Standard Cartridges if it is the first time you are using the elevator. Pull the chain again and return to the Hall of Seasons. The two doors will open as you approach them.
Back to the Hall of Seasons, you'll notice there are now some pillars moving up and down. These pillars will help you reaching the second floor of the hall. Shoot the skeleton first, to temporarly get rid of him. Climb to the pillar in front of the water button once it comes down. Pull up and consecutively jump to the left untill you reach the top of the fourth pillar. Standing jumps will do. You must jump when the pillar where you are standing is above the one to the left. Once you are over the fourth, wait until it goes up and jump to grab the big ring above and then pull up. You can walk over the second bar connected to the ring to reach the 2nd floor platform around the room. Jump/vault over the rails. At this floor, two skeletons will break from the wall. You can either pull them off the ledges to get rid of them or simply ignore them by running by. Note that you can pull them anywhere and not just from edges without rails. If you head left a skeleton will break from the wall. You can avoid this from happening if you don't go left, as it takes some time to pull him off the ledge. Go right. Another skeleton should break through the wall. Run to the other side and go up the stairs to the 3rd floor. Ignore the door on the right for now and head around the third floor to the left. There are two skeletons walking around here. Once you reach the other side of the broken floor, climb the left surface to the right to reach a small ledge with a lever. Release the surface once you are above the ledge. Pressing the lever will open the door near the stairs just below. Return to that door by using the surface to return to the floor and going all the way around. Inside you'll find V-Packer Standard Cartridges. You have to push the left wall in order to get a strength update. Collect the Large Health Pack and return to the small edge where you previously pressed the lever. You are about to leave the Hall of Seasons. Once you are standing near the lever, climb the wall all to the top. As soon as Lara turns around to start swinging, immediately locate and head to a small platform on the left side to recover your grip bar. Jump back to the ceiling and continue the way to the left, all the way to the top trough the crack in the dome. Once you pass the opening, immediately jump backwards. It may be a bit hard to do this because you cannot waste any time while climbing, otherwise the grip bar will end before you can reach the top. Approach the door at the right and it will open. Go left and another door will open. Go up the stairs. You will be now entering the room with the infamous boss, the Red Ghost. Pass the next door. After the sequence the battle will start immediately. Your notebook gets an update here as well.
This leads you to your next boss battle, Brother Obscura. Good luck!