Darksiders Warmastered Edition

To obtain the Abyssal Armour Set you need to collect 10 Abyssal armour pieces accross the game.

Below is the location list for each piece and also a video thanks to Darksiders Wiki and 【XCV//】on YouTube.

1 - Twilight Cathedral - After you collect the three swords to raise the circular platform up out of the floor (where you access the door to the end boss), turn around and hop up the pushable block onto the balcony. To the left is a door with a Goremaw above it. Use the Crossblade to stun it and run through the door to claim the armour piece and some other toys. (It is also possible to use a bomb from the lower level if you do not wish to return later, the timing is tight however)

2 - Scalding Gallow - As you leave the Library, on the right hand side you will see a platform you cannot reach. On one of the pillars of this platform, there is a red growth with a bomb conveniently attached to the growth. Throw a car, or any other object, at the bomb, and the explosion will cause the pillar to fall, allowing you to reach that platform. You can also use your Crossblade, but the car is probably easier, so you can get the piece right when you get there.

3 - Scalding Gallow - Standing by the Vulgrim location and looking over at Samael's prison you will see a small path. Do a single jump towards it and when you are about half way down, glide forward against the wall until Shadowflight deactivates. Follow the path up to chest and the Abyssal piece, then jump out and use the Shadowflight point to get back up.

4 - Drowned Pass - Before doing the shadow challenges (or afterwards if you miss it) dive underwater near the entrance to this area (to the left) to find the armour piece in one of the caves. You actually go to this cave during the shadow challenges but you can't open chests in the real world while in the Shadow realm.

5 - Drowned Pass - After completing all shadow challenges you'll get this given to you automatically by the Tormented Gate at the end.

6 - The Hollows - As you progress through this level, you will be in a tunnel where a Gholen Demon smashes through the right wall to attack you. The armour piece is where the demon smashed through the wall inside a small room.

7 - Iron Canopy - After fighting the first Loom Warden, you'll find yourself in a room with a Chronosphere and a red grapple point above it. Abyssal Chain up to find the armour piece.

8 - The Ashlands - Ride to the cliff east of the three connected mining towers in the Ashlands to find a shadow flight point. Up here is a Soldier Artefact and some Abyssal Chain points (red) use these to get onto the roof of the drilling tower where an armor piece is located.

9 - The Black Throne - Head to the third wing of the Black Throne (where the third Guardian resides). At the bottom of the long spiral staircase you come to is a clump of red crystal. Shoot the nearby window portal on the wall. To the north is a chasm with a spinning block floating above it. Charge a shot and shoot the window on the spinning block with the Voidwalker.
Now, wait by the first portal until the spinning block portal faces north -- you should be able to make out a Bomb Growth in the distance. Hop through and float down to get to the northern ledge.
A Bomb Growth is on a column ahead. You can snag a bomb by using the Abyssal Chain.
First, create a portal on the nearby window. Snag a bomb and wait by the portal. When you see the red crystals appear, toss the bomb through the portal to destroy them. You can now use the portal to access a chest with an Abyssal Armor Piece inside.

10 - Eden - On the way towards the Tree of Knowledge, immediately after crossing the bridge that requires the Mask of Shadows to pass, take a right onto the water. Find the waterfall at the very edge of the farthest island and walk through it. Activate the Mask of Shadows to see the chest and claim your final piece of armor. If you missed it don't worry if the in-game conversation indicates no return. The portal next to Azrael in Leviathan's Drift can take you back there anytime.

The video below has timestamps for each location for easy navigation.