Walk forward and the big gate will open. Go down the stairs and turn right. There is a movable part of the wall you can push. Do that to reveal a room behind. Pick up the two sets of Vector-R35 Clips from the floor and pull the lever to open a gate on the other side of the room and raise a bunch of logs in the deep pit.

Return back to the pit and stand in the middle of the edge. You have to make your way across jumping on the logs, but this is not as easy as it seems. The logs are moving because of the Breaths and you can easily fall into the deep pit. You may find your own way, but here is one:

Getting across - (The logs you need to jump onto are shown in this screenshot.) With the entrance to your back, stand in the middle of the ledge. You will hop to the log ahead, so keep in mind this: to avoid hopping on the left or right side of the log and falling to your death, press slightly the up or down cursor key. Lara hops to the direction of the last command. If the last cursor key you pressed was the right one (for instance), Lara will hop to the right. Face the direction of the log, but do not turn Lara to the left and right in order to line her up with the log. Just face the direction of the log. When you see it in front of you, hop on it, pressing Action whilst in midair to grab the log in case Lara does not eventually reach it.

You need to jump to the log diagonally to your left, so turn 45 degrees to the left. Again, face the general direction of the log, and when you see it lining up to Lara, jump. As before, press Action whilst in midair to grab the log if Lara does not reach it. Turn right to face the log in front of the head. You need to hop on it, so as before, face the direction of the log, wait for it to line up to you, and hop. When you do that, the head on your left slides back, revealing an alcove. Jump in the alcove and pick up the Large Health Pack and the two sets of V-Packer Cartridges.

Return to the last log. You can either hop or jump on it taking some steps backwards first. You now have to jump to the very last log. You may have to grab it and pull up. If you cannot jump on the very last log, use the previous one (see this screenhot to get oriented). Finally, jump towards the stairs. Get the Air Crystal and return to the pit.

Your way back - There are no more breaths now, but this does not necessarily make your way back easier, because the logs keep moving. The left way seems easier to leave. So, go to the far left side of the ledge and take a standing jump to the log ahead. There are two logs on your left. Take a standing jump to the second one (it looks like it is close to the far left corner of the pit). From there, either jump to grab the ledge that leads to the exit, or jump to the very last log and finally, jump towards the exit (this screenshot shows the way). Head up the stairs and pass through the hallway to return back to the Hall Of Seasons.