BELOW

I don't wish to spoil too much of the mystery of this game, but this solution should still be considered as mild spoilers.

First, find the shortcut that will let you easily access this area. In the very central room of the 4th floor, you'll find a glowing floorpad. This will activate a teleport shortcut back to the grassy plain above the beach that you can use to access the start of this sequence. Fair warning: you might need it a lot. Prepare well with food, +bandages, and ideally a few stews (cooked with water and meat) to keep hunger and cold at bay, as there's a long while with no fireplaces.

Going forward from the teleport room, you will open a monolith and proceed down a series of lifts. At the very bottom level, open another monolith to receive a latern upgrade. Use this upgrade to activate the switches as you proceed back upwards, fighting a boss on the top level before you can escape. The achievement pops once you leave the area.

Note that if you die (as I very often did), you lose the upgrade and have to collect it again.

Great solution above but I wanted to add a few things about the boss fight since you don't want to repeat it.

Video not mine, no credit:



When you reach him he will stand up. Try to get a few wacks in like the video does. I think it's roughly 6 hits to make him drop so you can hit his insides. Next he will either do a shield/shock wave attack or laser eye attack. Both are easy to dodge if you watch the video and do what he does.

Now where I differ from him and beat the boss a lot faster was to : Always be confident in your attacks. When he hits the wall, run up and hit him non stop even if he spins around and looks at you. He should be stunned before he can damage you so don't run away like the video does and you get a good 6-8 more hits a charge (if you see the shockwave starting up, retreat and return if he opens up) . When he starts to stand up you need to hit him a few times to make sure that the next charge he will drop again. Retreat before the shock wave and repeat.

You can tell when you hit the boss because it will have a red slash. You can tell when you've damaged him (1/6 hits needed to open up) when you see nothing but a yellow slash. I played it safe and never tried to drop him while he was doing a shock wave. Immediately when he drops you need to run to the elevator you didn't just get off. You need to keep running because if you are like me, you are starving/freezing at this point.

When you see the cut scene for a new light being added to your latern, and the monolith closing, you have got your achievement.