In order to unlock each artifact (other than Rebirth, see that section for more details), you will have to complete a challenge in Bulwark's Ambry. To access this hidden realm, travel underneath the map in Sky Meadow and input a pattern, then confirm on the screen behind the pattern input area (You do not need to see the pattern to input it). If you entered a correct pattern, the teleporter will open a portal. If you enter an incorrect pattern it will fail and you can try again.
(Note: Upon entering the portal, the artifact you are trying to unlock will be active for this stage, then disable when leaving the stage. If you are planning to continue your run, be aware of this, as some artifacts may alter your run, such as Meta changing your survivor.)

Once in Bulwark's Ambry, you will find an Artifact Key in this location. Pick it up, move to the center orb, and use the key.

Monsters will begin spawning and the orb will begin shooting as well. The orb can only be damaged by Artifact Keys.

Killing monsters gives a chance to drop more Artifact Keys to grab and attack the orb with (No need to wait and collect a lot of keys, no matter how many you use at one time, it will do the same amount of damage. It is best to attack as soon as you can after grabbing an artifact key).

Once the orb has no HP remaining, all monsters will disappear and you will be able to grab the artifact.

After grabbing the artifact, a portal will appear to return and start a new loop.

Artifact of Spite
Enemies drop multiple exploding bombs on death.

Pattern:
🔺🟢🔺
🟢🟢🟢
🔺🟢🔺
[Triangle, Circle, Triangle]
[Circle, Circle, Circle]
[Triangle, Circle, Triangle]

Pattern Location: Settings Screen.
On the right side beside the pod. It is easier to see if you change the setting LOD Bias to Custom (Thanks chinほ).

Artifact of Command
Choose your items.

Pattern:
🟪🟪🟪
🟪🟪🟪
🔺🔺🔺
[Square, Square, Square]
[Square, Square, Square]
[Triangle, Triangle, Triangle]

Pattern Location: Bazaar Between Time.
In the reflection behind the shopkeeper.

Artifact of Delusion
Risk your items after completing the Teleporter event in a test of memory to gain more items.

Pattern:
🟪🟢🟪
🟢🟢🟢
🟪🔺🟪
[Square, Circle, Square]
[Circle, Circle, Circle]
[Square, Triangle, Square]

Pattern Location: Devotion Update Teaser Video
Highlighted shapes seen in the background for the text box on screen starting at 0:11 in the trailer for the Devotion Update.

Artifact of Devotion
Replace broken drones with Lemurian Eggs. Give an item to hatch and gain a follower. All Lemurian followers receive item effect.

Pattern:
🔺🔷🔺
🟪🔷🟪
🔷🔺🔷
[Triangle, Diamond, Triangle]
[Square, Diamond, Square]
[Diamond, Triangle, Diamond]

Pattern Location: Twitter Post[x.com]
@RiskofRain posted an image on Twitter of the artifact code.

Artifact of Honor
Enemies can only spawn as elites.

Pattern:
🟪🟪🟪
🟪🔺🟪
🟪🟪🟪
[Square, Square, Square]
[Square, Triangle, Square]
[Square, Square, Square]

Pattern Location: Sky Meadow.
Left of the pattern input area for the artifact teleporter.

Artifact of Enigma
Spawn with a random equipment that changes every time it's activated.

Pattern:
🔷🟪🟪
🔺🟪🔺
🟢🔷🔷
[Diamond, Square, Square]
[Triangle, Square, Triangle]
[Circle, Diamond, Diamond]

Pattern Location: Bulwark's Ambry.
On the giant cube in the distance.

Artifact of Chaos
Friendly fire is enabled for both survivors and monsters alike.

Pattern:
🟢🔺🟢
🟢🔺🟢
🟢🔺🟢
[Circle, Triangle, Circle]
[Circle, Triangle, Circle]
[Circle, Triangle, Circle]

Pattern Location (1/2): Abandoned Aqueduct.
Between one of the tar pits and the tunnel.

Pattern Location (2/2): Abandoned Aqueduct.
Inside the Ancient Gate.

Artifact of Glass
Allies deal 500% damage, but have 10% health.

Pattern:
🔷🔷🔷
🔷🔷🔷
🔷🔷🔷
[Diamond, Diamond, Diamond]
[Diamond, Diamond, Diamond]
[Diamond, Diamond, Diamond]

Pattern Location: A Moment, Fractured.
Behind the Obelisk

Artifact of Dissonance
Monsters can appear outside their usual environments.

Pattern:
🟢🟪🟪
🟪🟪🟪
🟪🟪🟢
[Circle, Square, Square]
[Square, Square, Square]
[Square, Square, Circle]

Pattern Location: Abyssal Depths.
On one of the high platforms near the ceiling.

Artifact of Evolution
Monsters gain items between stages.

Pattern:
🔷🔷🔷
🟪🟪🟪
🟢🟢🟢
[Diamond, Diamond, Diamond]
[Square, Square, Square]
[Circle, Circle, Circle]

Pattern Location: A Moment, Whole.
On the Twisted Scavenger.

Artifact of Metamorphosis
Players always spawn as a random survivor.

Pattern:
🔷🟪🟢
🔷🟪🟢
🔷🟪🟢
[Diamond, Square, Circle]
[Diamond, Square, Circle]
[Diamond, Square, Circle]

Pattern Location: Titanic Plains.
On one of the stone arches in the distance.

Artifact of Rebirth
Descend to Petrichor V with gifts from a previous life.

This artifact is different from the rest and cannot be earned through the artifact teleporter to Bulwark's Ambry.
You must find a Halcyon Shrine, activate it, and complete the trial. After that, enter the green portal that appears. Continue activating teleporters and entering the green portals until you arrive at the Prime Meridian. Head up to the top of the area and defeat the False Son, then offer an item to the Shrine of Rebirth. The artifact should unlock after doing this.

Artifact of Sacrifice
Monsters drop items on death, but chests no longer spawn.

Pattern:
🔺🔺🔺
🔺🔺🔺
🔺🔷🔺
[Triangle, Triangle, Triangle]
[Triangle, Triangle, Triangle]
[Triangle, Diamond, Triangle]

Pattern Location: Gilded Coast.
Underwater in the lake near the center.

Artifact of Vengeance
Your relentless doppleganger will invade every 10 minutes.

Pattern:
🔷🟪🟪
🔷🟢🟪
🔷🟪🟪
[Diamond, Square, Square]
[Diamond, Circle, Square]
[Diamond, Square, Square]

Pattern Location: Logbook.
Under the diorama of the logbook entry for the environment Hidden Realm: A Moment, Fractured.

Artifact of Kin
Monsters will be of only one type per stage.

Pattern:
🟢🔺🔺
🔷🟢🔺
🔷🔷🟢
[Circle, Triangle, Triangle]
[Diamond, Circle, Triangle]
[Diamond, Diamond, Circle]

Pattern Location: Distant Roost.
On a ledge near the top of the map.

Artifact of Swarms
Monster spawns are doubled, but monster maximum health is halved.

Pattern:
🟢🟢🔺
🔺🔷🔺
🔺🟢🟢
[Circle, Circle, Triangle]
[Triangle, Diamond, Triangle]
[Triangle, Circle, Circle]

Pattern Location: Rallypoint Delta.
On the island in the lake.

Artifact of Death
When one player dies, everyone dies. Enable only if you want to truly put your teamwork and individual skill to the ultimate test.

Pattern:
🟢🟢🟢
🟪🔺🟪
🟢🔺🟢
[Circle, Circle, Circle]
[Square, Triangle, Square]
[Circle, Triangle, Circle]

Pattern Location: Wetlands Aspect.
At The Altar of N'kuhana in the cave under the stage.

Artifact of Frailty
Fall damage is doubled and lethal.

Pattern:
🟢🟢🟢
🔺🟢🔺
🔺🔺🔺
[Circle, Circle, Circle]
[Triangle, Circle, Triangle]
[Triangle, Triangle, Triangle]

Pattern Location (1/2): Siren's Call.
Toward the left side of the cliff.

Pattern Location (2/2): Void Fields.
At the bottom of the slope leading to the portal.

Artifact of Soul
Wisps emerge from defeated monsters.

Pattern:
🟢🟪🟢
🟢🔷🟢
🟪🔷🟪
[Circle, Square, Circle]
[Circle, Diamond, Circle]
[Square, Diamond, Square]

Pattern Location: Scorched Acres.
On one of the hills in the circular stone structure (this one is different from the others and uses objects instead of a tablet showing the symbols). There is a shape missing from the pattern, but the circle object can be seen close to the structure.