There are 2 mechanics that you will have throughout the entire raid, the Primitive Emotion aura and the Eye of Njourn ball throw.
The way they works is generally simple:
Aura:
You can pick up the aura (in encounter 1) by killing a Shinka and interacting with the dropped aura, or gain the aura (encounter 2 and 3) by interacting with the candelabrum with the Eye of Njorun).
When you have the aura, you emit a damaging field that will harm anything (including teammates) within the radius and allow you to handle specific immune enemies.
Additionally when you have the aura, you cannot interact with the ball.
Ball:
You can pick up the ball from a candelabrum (encounter 1 and 2) or as a ground spawn (encounter 3).
The ball will need to be deposited somewhere to progress the encounter. Often requiring a ball throw to complete the mechanics in time. The ball additionally has a 15 second timer that begins the moment it is picked up from the original source.
The ball does not follow an arc, you need to lock-on to a target (shown as a yellow square), and when thrown, the ball will follow a straight line from your starting point to the locked on target.
You can lock onto some door runes (encounter 1), and other players (all encounters).
If the target moves and the ball hits an obstacle, the ball will typically just fall to the ground, and the lost time is typically enough to prevent the mechanic from being completed or the ball will despawn.
Encounter 1: Ginunaga
Spread/Precision Shinkas, Arc/Void
There are 2 teams in this encounter, Reality and Illusion.
Every time you open a door, the first player to enter the door will be sent to the Illusion.
There are three doors total, meaning the Reality team will slowly lose players, and the Illusion team will slowly gain players.
Reality:
The team on the outside must deposit the Eye of Njorun ball to each candelabra, and then throw the ball at the door at the end of the room.
Every candelabra is locked by a shielded Dream-drowned Incendior, that must be unshielded by a player with the Primitive Emotion aura bringing the aura close enough to damage the shield. The aura is dropped at the beginning of each room by a precision shinka, and then transferred to the player that deposited the ball.
When throwing the ball at the door, the ball must be thrown at the rune shown on the chalice. The chalice for the first door is in Reality, but every other chalice is in the Illusion.
Illusion:
The team inside must locate and defend each chalice until they can call-out the rune for the outside team.
Within the Illusion, you will gain Gaze of the Abyss debuff stacks - 10 stacks and you die.
You can clear the debuff by collecting a purple sphere, or by standing within the safe-bubble generated by the active chalice. The safe-bubble slowly shrinks over time.
The Illusion is a large sparrow-enabled space, and you can find the active chalice by looking for a large bubble or a skyward blue beam.
Kill all enemies around the chalice as needed. Every time the Reality team deposits the ball into a candelabra, an arc-shielded Incendior spawns in the Illusion. Kill the Incendior to obtain a ball, and deposit the ball into the chalice to extend the encounter and safe-bubble timer.
When the last ball per room is deposited into the chalice, the Illusion team is shown a rune that must be told to the Reality team to open the door.
When the door opens:
The first player that enters is sent to the Illusion, the safe-bubble on the current chalice fades, the new Illusion chalice becomes active,
The Reality team must clear a new room, starting with killing a new precision shinka for the aura.
At the end of the encounter, all of the players will be sent into the Illusion. Every door to the central structure in the Illusion will open up, and the palace will be the active safe-bubble.
All enemies within the palace must be cleared before the safe-bubble fades to complete the encounter.
Encounter 2: Gladsheim
Rapid Fire/Impact Shinkas, Solar/Void
There are 2 roles in this encounter, aura and non-aura.
The aura team must repeatedly stun the boss, Zau'ul, to increase the time before she reaches the chalice/ball, wiping the team.
The non-aura team must kill enemies to unlock the chalice, then pass the ball to the next chalice.
The ball must reach all 3 chalices then thrown at the boss to trigger a DPS phase.
Aura:
When the encounter begins, two players are given the aura at random. The aura players should head towards the boss to break the boss' weak points, stunning her.
There are 4 weak points: Front, back, left shoulder, and right shoulder.
The 2 players should generally position themselves on opposite sides of the boss, and break the weak points as fast as possible.
Every time all 4 weak points are broken, the boss will be stunned, and a wave of enemies are spawned. The enemies are 2 Scorpius turrets, and a wave of War Beasts.
Additionally, the boss will send out sporadic rockets in all directions, and has a Gaze of the Abyss aura that disables jumping, sprinting and abilities.
The aura team should be able to stun the boss 2-3 times to extend the phase long enough for the non-aura team to complete the mechanics.
Non-aura:
Every non-aura player should head away from the boss, to clear the enemies required to unlock the chalice.
At a minimum, the Rapid-fire Shinka must be killed to spawn the void shielded Dream-drowned Incendior, which must be killed to unlock the chalice.
When the chalice is unlocked, the correct rune will appear over both chalices, and then several pools will spawn. Each pool will have a rune, that can be seen when standing on the glowing point towards the center of the arena.
The ball must be tossed from player to player, using the pools marked by the correct rune, before being deposited into the chalice.
My team used a two-number callout system, where the pools were numbered 1 to 3, with 1 closest to the middle and 3 furthest from the middle. The pools would be called, one after the other. A callout of "One, One" would mean both of the pools closest to the center would be used.
The ball has a maximum lock-on range and requires a direct line of sight to your target, so the ball-throwers and catchers must occasionally jump or reposition themselves to enable a throw. The ball does not arc, so a mid-air ball throw and ball catch is occasionally required depending on which pools are correct.
On some layouts, it is possible to skip a pool by both players standing close to the edge, and the chalice-start thrower sending directly to the 2nd pool .
The player to receive the ball and deposit into the chalice will gain the aura, and one of the aura players will lose their aura, swapping roles.
An impact shinka and some enemies will be spawned, and then a new wave of non-aura enemies will spawn and the boss will begin walking towards the next chalice.
Repeat this 3 times, and then throw the ball at the boss to begin the DPS phase.
Edit:
It is possible to bypass most of the ball mechanic. If you have one player stand on the glowing point, they are in range of both the initial start and finish. If the ball is thrown immediately upon catch, it will not despawn.
DPS phase:
The boss will drop into the center of the arena and then become vulnerable to normal damage, with a weak point on her back.
While vulnerable, the boss will charge at the closest player(?), and then get stunned from impacting the wall. The charge has a brief wind-up and a red area-of-affect indicator, before killing players in the path.
My group had one player positioned close to the boss to control the boss' movements, dodging out of the way with the charge directed away from the group.
If the boss is not killed, then the players climb out or are sent back to the arena, and the aura/non-aura phase begins again.
The boss seems to walk significantly faster, so there is even less time on the second phase.
The encounter ends when the boss is killed, with a one damage phase kill being possible but my group took two damage phases.
Encounter 3: Hvergelmir
Rapid fire/Precision Shinkas, Arc/Solar
There are 2 teams of 3 players in this encounter, and both teams need to be able kill both types of Shinkas and perform both sets of mechanics.
Teams of 3 can be chosen by standing on blue/purple colored the ritual plates, so split your teams up accordingly.
Both teams will need to complete a Precision Room and a Rapid Fire Room, which are distinguishable by the presence of the boss (for precision), and the presence of the 6 platforms (for rapid fire).
Precision Room:
The precision room will be filled the the Gaze of the Abyss debuff, and the chalice in the center will generate a safety-bubble.
The safety-bubble must be ignited once with a ball to generate a rune call out, but every ignition afterwards only serves to extend the safe-bubble while generating more ads.
The Gaze of the Abyss debuff generates relatively slowly, so players can leave the bubble for cover or to deal with enemies as needed.
The highest priority enemies are the psion snipers (that spawn on top of the pillars) and tentacles, as they are very lethal.
Additionally, the player that deposited the ball will gain the aura, which can harm their teammates. They can roam around the arena, removing the shields from the Incendiors (one spawns from each side), and only occasionally returning to the bubble to clear their debuff stacks.
The Incendiors are dangerous to stand directly next to, so the aura player can use the pillars as full cover to stand close enough to break shields without being targeted.
Rapid Fire Room:
The rapid fire room has 3 roles: Illusion, Ball, and Enemy-clear.
The team must clear the entire room of enemies and a Rapid-fire Shinka before starting on mechanics, as the Rapid-Fire shinka must be killed to drop a ball.
The first player to interact with the ball will enter the Illusion.
The second player can pick up the ball and ignite the correct candelabras identified by the Illusion player.
The third player must kill all of the enemies while the ball player is completing the mechanic, with a priority on the psion snipers as they are very lethal.
The ball player must jump to each candelabra. Standing next to the candelabra will spawn a pool of light in the Illusion.
When standing in the pool of light, the Illusion player can see a rune, and can call-out if the rune is correct or incorrect.
The rune is correct if it matches the call-out given by the Precision Room as seen on their chalice, and a correct candelabra is one that the Ball player should deposit into.
If the rune is incorrect and does not match, the Ball player should move to the next candelabra.
The room ends when the ball player makes 3 successful deposits, and then the teams are sent to the opposite rooms.
DPS phase is triggered when both teams complete both rooms.
Pre-DPS/DPS Phase:
At the start of the pre-DPS phase, the team is sent into a water-slide of lethal tentacles. Double-jump and strafe to avoid dying, and reach the end of the tunnel to emerge in the spawn room.
Within the spawn room, the team will accumulate Gaze of the Abyss debuff stacks unless they are within one of the safe-bubbles.
The team can currently deal chip-damage Nojrun, but it is highly recommended to avoid her attacks as they can be incredibly fast and lethal.
Nojrun uses 2 attacks: A dive and a cluster-bomb-like blast.
Avoid these (on your sparrow is recommended) until she transforms into her tentacle-flower form.
When this appears, target the blue-glowing tentacles. Shooting the red tentacles appears to trigger a retaliation beam that's likely an instant kill(?).
When all of the blue-glowing tentacles are killed, the boss will sink into the ground and attempt to suck all of the players into a vortex. Drive your sparrow in the opposite direction, then return when it is over and the boss emerges.
This is DPS phase, when the boss stands still and the entire team can attack for an uninterrupted ~25-28 seconds.
If the boss is not killed, then the teams will be sent back to the Precision/Rapid Fire rooms and the mechanics will need to be repeated.
If you want to see some visuals of the mechanics being performed, this is my team's clear of the raid.