Tomb Raider I-III Remastered Starring Lara Croft

Done in TR1, St Francis' Folly. It's the room with all the swords.

I was able to get both Damocles achievements at the same time by loading my save, as the achievement trigger isn't until you leave the room.

Enter the Damocles room and pick up the key, then make a save. Run out of the key room and get hit by the sword, load your save.

This time walk out of the room and then carefully navigate it so that the swords don't touch you. Keep your camera pointing towards the ceiling and whenever you get close to a sword (one "square" away) then just take one step forward and wait to see if it falls. Use the pillars to your advantage as that's the distance you need to be for the swords to not reach you.

I believe there are 19 total (comment if you counted! Some swords in my game fell in the pillars making me uncertain, especially since more than one can fall at the same time). If you see no more swords on the ceilings anywhere, then leave. Both achievements should unlock at the same time once you exit the Damocles door and into the "main tall hallway".

Also tested: if you leave the room without defusing all of the swords, you can still go back and defuse the rest of them to unlock this achievement so long as you were never hurt by a sword at either time!