Ignore the closed door nearby and take the corridor leading west (the above screen), eliminating some Undead Scarabs on the way. Keep going west, but note the presence of a time portal. When you reach the western part of the destroyed fortress, look around for a Boatman Coin.
Select Phasewalker from the ability list and start activating the two "regular" (blue) portals in the area. The first one is by the lava (screenshot 1), the second in the north room (screenshot 2).
Stand in front of the first portal and use Death Grip on the handhold there - this way you'll jump into the portal without harm and be transported into a new place.
Turn west and grab onto the nearby edge. Move right and wall-run once you're on a small shelf - you'll reach the chest pictured above, which holds a random treasure.
You're ready to go back to the western part of the area. Locate the time portal (screenshot 1 shows the portal, screenshot 2 its location on the map) and activate it with Phasewalker. Step through the green portal to go back in time.
As soon as you use the portal, you'll be attacked by a new type of monster - a creature called Maelstrom. The best strategy against it is the same one used with Liches, which is trying to chase it into a corner to prevent it from doing too much of anything. Otherwise, Maelstrom will start throwing fireballs at you, and they're not easy to dodge.
Afterwards, take down Legion Soldiers in the area as well, and another Maelstrom too. Additionally, check out the south corridor to reach a hidden Boatman Coin. Return to the main area and locate the pressure plate shown above, on which you have to stand.
Make sure you're standing on the plate and activate Soul Splitter. Have the first half head for the north-western passage shown on the above screen (which had also been shown on a previous cutscene). Start wall-running to reach a large room.
There, you'll unfortunately be forced into another battle with a Maelstrom and Legion Soldiers. Attack Maelstrom first, even though he's much stronger than the Soldiers. Considering that otherwise you'd have to constantly watch out for fireballs, it's a much better choice.
After the battle is won, look around for a hidden Relic of Etu-Goth ([Lost Relics] side quest). Select Phasewalker, but DO NOT deactivate Soul Splitter. Activate Phasewalker on the regular portal where the screen shows.
Switch to the other half, go right and locate the second inactive portal (the above screen). Same as before, use Phasewalker. When the portal is activated, make sure you're standing right in front of it.
Switch back to the first half and locate a shadowbomb. Pick it up and approach the portal, BUT don't go through it. Instead, take a "look" through it and aim at the other half of the soul (the above screen) so that it could catch the bomb.
[TIP: If the process of swapping the shadowbomb between the two halves fails, make sure you've activated only the regular portals on both sides (not the reinforced ones!) and that you've aimed at the other half correctly (the marker changes colors).]
Take control over the second half of the soul - the one that caught the shadowbomb from the other side - one last time. Go south, past a fossilized form of Death, and take the stairs to the east. Stand as seen on the screen and throw the shadowbomb at the yellow crystals to blow them up.
Deactivate Soul Splitter and return to the time portal to go back to the present. Approach the platform on which the yellow crystals stood in the past and notice that you can now get to a chest with a Skeleton Key inside.
Take the south corridor and then turn east, but stop at the second time portal mentioned and ignored earlier - its location is displayed on the above screenshots. Use Phasewalker there and go back to the past.
Once you're in the small chamber, look inside the first chest. Bash every object you see - that should cause a second chest to appear (with a rare treasure). Afterwards, take the corridor leading east and turning north (the above screen).
Be cautious, because as soon as you approach the door outlined in the distance, monsters will show up in the area. Similarly to the previous battles, I recommend taking out the Maelstrom first and only then the Legion Soldiers. After you win, use the Skeleton Key to unlock the closed door.