The achievement/trophy requires you to "Get to the bottom of the Tomb of the Ancients in 3 minutes or less." This path takes less than a minute, even if you don't do it perfectly. So there's no need to stress out. Just focus and quick-save as you go. Also, make sure you don't overwrite your level-start save, in case you make a mistake and need to retry.
Follow the tunnel from the starting point to the hole. Run off the edge, and Lara should grab. Drop down onto the beam, then to the floor.
Approach the tunnel opening and hold Space/Y/Triangle (not sure what on Switch) to skip the cutscene.
Hang from the edge and climb down the textured rock wall...
...just far enough so you can drop onto the green ledge below.
Walk toward the edge nearest the wooden beam and shoot the bat.
Quick-save then take a standing jump onto the beam. (Or jump, grab, and pull up.)
Jump into the tunnel.
Run forward into the hole. Run off the ledge below.
Then drop down into the room near the broken bridge.
Step out onto the bridge and turn left.
Stand facing the railing, as close to the doorway as possible. Then vault over the railing...
...to land on the narrow ledge that runs along the wall.
Hang from this ledge and drop to the sandy ledge below.
Walk to the middle of the sandy ledge, hang from the edge, and climb down the rock face until you can safely drop onto the ledge below.
Quick-save, then position Lara as shown above and take a standing jump down to the ledge below, steering to the right while Lara is in the air to curve the jump a little. Take care not to run on off the edge when you land.
Walk to the end of the lower ledge and take a standing jump onto the jutting wooden beam.
Pull the lever to extend the rectangular ledges.
Take a short hop (Walk + Jump) from the beam to the first ledge.
Walk to the edge then take a regular standing jump to the second ledge.
Walk to the edge then jump forward and grab the third ledge; pull up.
Walk to the edge then take a short hop to down to the fourth ledge. Safety drop onto the fifth, directly below.
Ignore the sixth ledge (behind you), and just drop to the ground from here.
The achievement/trophy should unlock when Lara touches the ground. (Note that Lara's health loss here is from the undead knight, not from the fall.)
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