Tomb Raider I-III Remastered Starring Lara Croft

Done in TR2 - The Great Wall

Just like the rest of the game, use tank controls.

It's talking about the section after you move a push able block, slide down, fall in to a room with water and flying stones across the room. You need to get through that room without getting hurt but without using the ledge on the left, and without loading inbetween.

I'll explain my route with hopes that it will give some kind of guidance on how to achieve this - it'll take a few tries and depends entirely on the TV and sound latency. I have an LGCX running this at 120hz with a surround sound system, so my visual feedback is likely a bit faster than my audio one, so you may have to adapt my solution to your setup.

Thankfully you basically only have to dodge three of the five traps, as the other two can be avoided through easier means.

I refer to the trap locations geographically in terms of the way you should be facing to get through this room. Trap on the left signifies the trap beneath the ledge where the flints get fired right at the right wall. Trap in front is referring to the two traps you are facing when navigating this room, firing at the wall behind you towards the rooms entrance.
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Make a save point just before the slide.

After sliding down, I start the process by doing a running jump into the room to immediately dodge the first trap.

I then tap forward once to get closer to the second trap. When I "hear" the flint on the left being fired out, I hold down forwards until Lara wades forward three steps and past the second trap.

I then use the quieter clink of the flint fired from the front wall hitting the back wall as the moment to hold forward and wade for two steps past the third trap. I then tap forward once to get closer to the fourth trap.

Again I use the quieter clink of the flint fired from the front wall hitting the back wall as the moment to hold forward and get to treading water.

Then it's easy! Position yourself carefully so that you're at an even distance between the last two traps remaining as close to the wall as possible, then hold X to swim underwater. Swim UNDER the final trap and then carefully climb out of the exit.

The achievement will unlock the moment you climb out.

Tomb Raider II - The Great Wall (Level 1)

After moving a block and sliding down a slope, you will find yourself in flying blade trap room. The ledge you want to avoid is on the left. Line yourself up to the very left side of the platform angled straight forward. Then do a running jump and continue to hold Jump as you walk. If you stay perfectly on target (which can be hard with the analog stick, try the D-pad if needed) you should dodge all the blades in the front of the room as you go. Then you'll dive and you can resurface at the the ledge, climb out without taking any damage and the achievement unlocks.

Video:

I wanted to add another solution that I think might be easier for some people. It sort of builds a bit on a section of the other solution but It doesn’t require timing or anything.

When you get to the bottom of the slope, you want to line Lara up. Facing out to the water, you want to have her left side pressed up against the wall, then do a running jump.
The blades don’t start until you pass a certain spot, we can use that to our advantage.

As Lara lands, hold down the forward button so she starts moving as soon as she can. Be careful to keep her in a straight line, veering to the left or right at all will cause her to take damage.

When you get to the wall, carefully climb up, avoiding the disk shooter on the ledge, and that should be it!

Here’s a video guide I made in case anyone needs a visual: