These locations were extracted from: https://www.playstationtrophies.org/forum/darksiders/208486-...
In the western area of the map is a set of steps. Heading down these steps will eventually take you to a small pond. This artifact is found at the bottom of the water.
Once you drop down into the main section of the library, climb the broken shelves opposite. This artifact is found on the other side of the broken bridge. From the edge of the current side, glide across and you should just about make it.
On your way to The Dry Road you'll need to get past a fast closing gate. Activate the chronomancer point to slow down time, then the gate lever and quickly run underneath the gate. Follow the path and steps round until you reach a climbable wall. Climb as far as you can and then jump away from the wall to land in a pipe. Turn around and the artifact will be right in front of you.
Requirements: Abyssal Chain & Shadowflight
Before using the fan, it would be a good idea to activate the panel in the hallway before the fan, so that you can easily knock out another collectible after this artifact without backtracking too much. Onto the actual artifact.
While riding the rotating fan, look for a gap in the lower walls. Just after the blade you're standing on passes this gap, jump or glide through it and press R2 when the prompt pops up to grapple up to the ledge. Use the glide point to reach the much higher ledge and you'll see this artifact floating in the air.
Nearby the chest that appears after destroying the tombstones are three stone blocks. Drag the middle one to reveal a set of steps. The artifact is in the room at the bottom of these steps along with several enemies.
In the eastern area of the map, just past the Vulgrim location, is a set of steps. Descend the steps and find the artifact at the back of the room.
Requirements: Tremor Gauntlet
When travelling to The Broken Stair, you will pass through a tunnel with bats, two glide points and a blue rock formation. Jump down to the rock and smash it to reveal the artifact.
The Broken Stair:
Near the entrance of the area is a collapse on the right wall. Walk through the gap and you'll see the artifact at the edge of the debris.
After pushing the statue off the ledge, the already damaged ground below will fall through. Jump down the hole and explore this new area. When you find yourself at the top of some growth, jump away from the wall to hopefully grab the artifact which is floating in the air.
In a small room with lava and two glide points is an artifact floating in the air. Use the glide point to hover up into the air and collect it.
One of the three sword puzzles contains a rotating bridge. Make your way to the center and glide down to the lower right ledge where the artifact is resting.
As soon as you enter, walk forward and jump into the lake. Turn around and swim up to the small patch of land where this artifact can be found.
On the lowest level of the underwater ruins is a set of steps that you can climb, or rather swim up. You'll find the artifact on this new floor.
After destroying the red rock formation in the room with the gas pipes you will come to a room with a massive hole in the middle. Dive to the bottom to find the artifact.
After destroying the red rock formation on platform A, you will eventually be in a room with some cylinders. There is an artifact in this room but you cannot reach it until you raise the water in the next room. Once you have raised the level of the water return to this room to find the centre of the area flooded. Swim to the bottom, through the tunnel and then upwards to collect the artifact.
Shortly after acquiring the tremor gauntlet, you will be in a large room where you must punch a block across three platforms to reach a higher level. To the right of the final platform is a hole in the wall. The artifact is inside.
The Dry Road:
Near where you are attacked by the angels is a building in ruins. You'll find the artifact on a ledge behind this building.
Just a bit north from the first tower is a cliff. Walk round and use the glide point to get up there. There will be some growth nearby. Climb it to find the artifact.
After stopping the central drill, drop down the hole that it made to land in a lake. Dive straight down and you'll see the artifact just in front of you.
After defeating the giant worm you'll need to pass through a set of tunnels separated by a body of water to reach the Stygian. The artifact is found near the bottom of the pool.
Requirements: Abyssal Chain
You may have spotted this artifact after dropping down the hole the central drill created, but found it agonisingly out of reach. In order to reach it you'll first need to climb to the top of the central drill. Once up here you'll see a grapple point inbetween the two drills. Swing across to the next drill and activate the control to shut it down. Jump down the hole the drill made and follow the path round to reach the artifact.
The Iron Canopy:
After defeating the Shadow Warriors and Broodlings in the alley, climb up the broken fire escape. The artifact is straight ahead, on top of the small building. Glide over to collect it.
Requirements: Abyssal Chain
After defeating the second Loom Warden head into the next room where you previously defeated several enemies. Go through the door on the left and grapple up to the ledge. As you walk round the corner, you'll see the artifact at the edge.
Requirements: Crossblade & Abyssal Chain
During the cutscene after you defeat Silitha, you will both crash through a few floors. Once you regain control of War, activate the platform with your crossblade and grapple onto it as it raises. Jump off at the next floor and grab the nearby artifact.
The Black Throne:
Requirements: Shadowflight & Voidwalker
This is found in the opening area of the third tower. There are two voidwalker panels here. Activate the panel on the ceiling first and then the one on the wall. Jump through the portal on the wall, glide to ensure that you land on the ledge and collect this artifact.
This is found in the area where you need to switch the water using the voidwalker panels. The artifact is in the section where the water currently is. Swim down to collect it.
Requirements: Shadowflight & Voidwalker
This artifact is found in the area where you fought the Rot Maulers and buddies, but you won't be able to obtain it until you redirect the beam through this room. Use the glide point to make it to the ledge and use a voidwalker shot on the panels on the right to climb even higher. Look across to the platform to find another panel on top. Use a charged shot on this panel and jump through the previous panel to shoot up and collect the artifact.
If you need a video, here it goes: