The Lost Domain
Make your way down the tunnel and take the passage that leads to the right. Hop over the small platforms to the other side where there is a lever. When you jump across Lara will say her legs are stronger. Hop up on the walkway and follow it back across the room. Grab the full health kit on your way out. Make your way to the other passage until you come to the edge with a lever beside you. When you pull the lever, the door at the far end opens but it doesn't stay open long. You need to make your way across the stone platforms before the door come down again. Use sprint to make each jump and you will clear each jump no problem.
If you don't use sprint you will hang on each edge and it will take way too long. When you make it across in time continue along the passage way into the next room. Directly ahead of you will be some stones and a door at the far side. Jump over to the left side and climb a ladder there. Climb another to reach the broken bridge above you. Jump across the gap and then slide down the slope to the left. Jump off the slope and grab the ledge of the walk way directly across from it. Pull the lever and drop down to the stone platform. Make a diagonal jump from the stone platform over to the stairs and make your way up to the door. After the door opens, walk into to Eckhart's lab.