These locations were extracted from: https://www.playstationtrophies.org/forum/darksiders/208486-...
1. Requirements: None
Near the beginning of the area is a bomb attached to some growth that is blocking the way up. Lob a car or use your crossblade, if you have it, to destroy the growth which will also knock a pillar down. Climb up the pillar and open the chest to receive your first piece of the abyssal armour.
2. Requirements: Shadowflight
From Vulgrim's position, peer over the edge and you will see a narrow path spiralling around where you freed Samael. In order to land on the path, you will first need to perform a single jump and then start gliding when you are roughly half way across. The chest at the top of this path contains the armour piece.
3. Requirements: Crossblade
After inserting the final of the three swords, the platform will rise. Using the block that you pushed earlier, climb up to the ledge where the Goremaw is hanging. Throw your crossblade at it to stun it and quickly run through to the next room. At the far end of the ledge is a chest which contains this armour piece.
The Drowned Pass:
4. Requirements: None
As soon as you enter, walk forward and dive into the lake. Swim through the cave on the left to find a chest that contains this armour piece.
5. Requirements: Complete the shadow challenges
After talking to the cursed demon, he will reward you with an armour piece.
6. Requirements: None
Early on in the level when an orange gate temporarily blocks your progress, a Gholen will eventually crash through a wall. After defeating all the enemies, open the chest from where the Gholen crashed through for this armour piece.
7.Requirements: Abyssal Chain
Just a bit north from the first tower is a cliff. Walk round and use the glide point to get up there. Walk to the end of the cliff and use the two grapple points to make it across the gap. As you are walking up this cliff, look on the right for another grapple point, however, you will not be able to reach it from here. Jump or glide towards it and press R2 to grapple onto it and jump onto the walkway. Walk around to find a chest which contains this armour piece.
The Iron Canopy:
8. Requirements: Abyssal Chain
In order to obtain the second beholders key, you will need to use the chronomancer and grapple points to get past two Goremaws. In the small room with the chronomancer point, look up and you'll see a grapple point. Grapple up there to find a chest which contains this armour piece.
The Black Throne:
9. Requirements: Abyssal Chain & Voidwalker
After descending the cylinder of stairs, you will have to use the rotating platform and portals to get across to the other side. Once you have made it across, you will see a portal and a bomb in this room. Activate the portal now. When the activated portal on the rotating platform is directly opposite you, quickly grab the bomb with your abyssal chain and throw it through the portal you just activated. It should land on or near the crystal and destroy it. When the platform has rotated back to where the crystal was (you'll see a panel), jump through to find a chest which contains this armour piece.
10. Requirements: Shadow Mask
After crossing the bridge, walk through the lake instead of heading up the steps. In the north eastern area is a waterfall that you can walk through. You'll see an outline of a chest at the back. Activate your shadow mask to completely reveal the chest and collect the final armour piece.
Here's a video showing off: