As with the other element levels, you may want to save in a new slot before entering this one, since you can't leave until you've completed it. Step on the button with the air symbol in the MAIN ROOM of the HALL OF SEASONS to open the three nearby doors.
Run through the door on the right (with the air symbol on the inner sign)...
...and pull the lever.
The portcullises blocking the inner hallway rise. Run through before the undead knights get too many whacks in.
The next door opens automatically, leading into the BREATH OF HADES proper.
Approach the steaming pit and turn right.
Find the movable section of wall and push it to reveal a small room.
Pick up 2 Vector clips (1-2) and use the lever...
...to open the gate at the other side of the pit, where the AIR CRYSTAL sits, and raise some tall, swaying pillars for Lara to jump across. Return to the rim of the pit.
The "Two Steps a Hades" achievement/trophy requires you to use only two pillars and get all pickups. So that's what we'll do. Start by positioning Lara on the left side of the pit, a few steps back from the edge and facing the second pillar on the left side.
When none of the carved heads on the left are blowing air, quick-save. Then take a running jump without grabbing to (hopefully) land on that pillar. If you're consistently falling short, try adjusting Lara's starting position so she's a tiny bit closer to the edge. Also, remember you can steer her slightly in the air to stick the landing.
Now wait for the heads ahead and to the left to stop blowing. Then take a short hop (Walk + Jump) to the next pillar (i.e., the third one along the left side of the pit).
Lara's weight activates a mechanism that retracts the stone head just to the left.
Jump into the alcove and pick up a large health pack (3) and 2 boxes of V-Packer shells (4-5).
Walk to the edge and face the pillar you just came from. Wait until the head on the left is not blowing, then take a short hop (Walk + Jump) onto the pillar.
Turn left and line Lara up facing the left side of the ledge in front of the alcove, between the carved head and the next pillar. It may seem counter-intuitive, but I found it helps to aim a little to the right of where you actually want her to grab, as shown above. Wait for the dragon heads ahead and to the left to quiet down. Save again if you like. Then jump forward, steering just a little to the left in the air...
...then grab the ledge.
Pull up, climb the steps, and take the AIR CRYSTAL (6). When you do, the gate at the entrance re-opens, and the dragon breath ceases.
If you're going for the "Two Times a Hades" achievement/trophy, you'll need to use the same 2 pillars for the return trip. So move down the stairs, line up a jump from the ledge onto the nearest pillar on the right (i.e., the one closest to the alcove where you found the last few pickups). Save again. Then take the running jump.
Walk to the far side of this pillar. Wait for the next pillar to lean to the right.
Then take a short hop (Walk + Jump) to land on it.
Walk to the far side of this pillar. Line up a jump to the right side of the ledge at the base of the steps, and save again. Wait for the pillar Lara is standing on to lean toward the stairs. Then jump forward...
...grab the ledge, and pull up.
Proceed through the gates back to the HALL OF SEASONS.
The achievement/trophy should unlock as the level loads.
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