2 Man Sanctified Mind

My preferred composition for this challenge is 1 titan and 1 warlock. Most compositions can work once you are more experienced with the fight, but I have found 1 titan and 1 warlock to be the easiest.

Titan:

The titan should be on Ward of Dawn (top tree void)

No specific exotic armor is required, but dunemarchers can be useful in clearing out enemies quickly. You also want to have as many Enhanced Relay Defender mods on as possible to increase your damage. Note that these mods can only be applied to Garden of Salvation armor. If you have the choice of using an exotic armor piece or an extra Enhanced Relay Defender, personally I would recommend the extra Enhanced Relay Defender, but it's really personal preference and you can make a decision after a few attempts.

As for other mods, sniper rifle finders and scavengers, as well as grenade launcher finders and scavengers can be useful. I recommend at least 1 concussive dampener mod on your chest piece to reduce damage from cyclopses and the boss. Seasonal mods, such as Oppressive Darkness or Breach and Clear, can also be useful.

Warlock:

The warlock should be on Well of Radiance (middle tree solar)

Like the titan, no specific exotic armor is required. Transversive Steps or Necrotic Grips can be useful, but it's down to personal preference. Like the titan, using as many Enhanced Relay Defender mods as possible is important. Again the decision between an extra Enhanced Relay Defender or an exotic armor piece is up to you, but warlock exotic armor pieces do not provide as much utility as titan exotic armor, so the extra damage of another relay defender is probably the right choice.

Your other mods will be the same as the titan.

Weapons:

Both players will be using the same weapons. You will want to start on Wendigo-GL3 (Interference VI will also work if you do not have Wendigo, but it is not as good). You will also want to use Trinity Ghoul with its catalyst, as well as a kinetic sniper such as Succession. You will want to have another non-exotic energy primary, as well as Izanagi's Burden with catalyst ready in your inventory. 

You will want to start the encounter and use Trinity Ghoul to clear the waves of enemies that spawn until the boss's weak spots are available to shoot. At this point you will shoot his left weak spot to open up the blue portal and the player assigned to go in first will enter the portal. 

The person in the main arena has the job of using Trinity Ghoul to clear out enemies and prevent any goblins from sacrificing. Remember that every time a portal is opened, a cyclops will spawn on the corresponding pillar. These cyclopes are very high priority targets, as they can do massive damage and potentially one-shot you if not dealt with quickly. Their attacks can be avoided for a little while by moving around a lot if you need to kill any goblins that are close to sacrificing, but try to kill them as soon as possible with your sniper. 

The person in the portal has the job of using Trinity Ghoul to collect 10 motes as fast as possible. You will get faster with practice, but the sooner you can collect the 10 motes, the better. As soon as you have collected all 10, inform your partner so they can shoot the weak spot to bring you back to the main arena. While you personally cannot hold more than 10 motes at a time, after you have told your partner to pull you back, it is useful to kill any remaining enemies because when your partner goes into the portal, they might be able to pick up any left over motes, speeding up their process.

Once 10 motes have been collected, the person in the main arena should use their sniper to open the portal and go into it themselves. If there are any newly spawned enemies near the boss, it can be helpful to shoot off a trinity ghoul shot to clear some of them for your partner. The person who is pulled back to the main arena will deposit their motes and both players will switch jobs, with the returning player using their Enlightened buff to kill the shielded goblins. Remember to kill the cyclops soon after returning to the arena.

30 motes must be deposited in each portal to get to damage phase. This means someone will have to enter each portal 3 times. The first person will go in the first portal, then the second person will go in, then the first person will go in again. After the first person has been pulled out of the portal, the second person will open the right-side orange portal and repeat the same steps as before. Note that at this point, two cyclopss will spawn in quick succession, so have a plan for how to deal with both of them at the same time. Then the first person will go in the right side, then the second person will go in again, and once all motes have been deposited, you will have to do the tether mechanic to start the damage phase. Remember that if a goblin sacrifices at a pillar, it will remove 5 motes. It is possible to go into a portal for a 4th time and recover lost motes, but it is very difficult and both players must be extremely fast to pull it off. If a goblin sacrifices at either pillar, it is most likely a wipe. 

To start damage phase, you must tether from the correct pillar to the boss. When the boss opens his hand, signaling that you are able to tether to it, both players should swap to their non-exotic energy primary and Izanagi's Burden. If you are low on sniper ammo, you have some time to find some around the arena. If a wave of enemies has just spawned, kill all of them before tethering. If it has been a little while since the last wave, wait for them to spawn, kill them, then tether. Right before you begin the tether, the titan should place a bubble in between the two pillars. 

Tethering to the boss can be difficult, and depending on the positions of the pillars and the boss, it may be impossible, however this is rare. Have the person assigned to be at the front of the tether get in position near the boss. Open the tether, have the base walk into position, then synchronize your jumps so you are both floating in the air for a few seconds at the same time. This is the best way to make the tether reach all the way to the boss. This will take some practice to do consistently. Experiment with moving forward and backward to get a feel for how far from your partner you can be while still being connected by the tether. Also note that in the first phase, the person at the front of the tether will be hovering over the vex milk, and in later phases both players will be hovering over it. This means you cannot spend much time on the ground, which can make synchronizing your jumps difficult.

Once you have successfully connected the tether, both players should run through the bubble to the opposite pillar, the warlock will place their Well of Radiance, and you can begin damaging with Izanagi-Wendigo hotswaps. There are a few possible damage rotations, but the one I have found to be the best is to shoot a total of 4 Izanagi shots and 9 Wendigo shots, alternating between 1 Izanagi followed by 3 Wendigo. 

If you are not comfortable quickswapping, there are a number of guides available online but the general idea is that sprinting at the same time as you swap weapons will cancel the animation of pulling out your weapon. With Izanagi and a grenade launcher, this swap is done immediately after the first part of Izanagi's reload animation, where the bullet is loaded into the gun, and then it is done again after shooting the desired number of grenade launcher shots. Remember that Wendigo has the perk Auto-Loading Holster, so when you are out of ammo, wait a little longer than you normally would before swapping back to it after shooting your Izanagi shot so it has time to reload itself. Izanagi-Wendigo hotswapping is a skill in and of itself, and it will take practice to learn if you don't already know how to do it.

After the damage phase is over, both players will swap back to their initial weapons and repeat the process. It is possible to rebuild platforms in the window after damage phase, but you will likely find that it is not worth the effort since they will be taken away again very quickly. You will have a total of 4 damage phases before the boss will enrage, causing a wipe, so you should be doing at least 1/4 of his health per phase.

When the goblins are approaching the pillar, they may teleport. If you are not expecting this, you may not be prepared to kill them as fast as you need to. It is possible that some goblins will teleport to a spot on the opposite side of the pillar from where you are and begin sacrificing. If this happens, remember that as long as lightning rod is activated on your Trinity Ghoul (indicated by a buff called "lightning rod" in the bottom left of your screen), you can shoot the ground behind the pillar and the lightning will chain to any sacrificing goblins. This will allow you to kill them much faster, and from much farther away, then you otherwise could, and will likely save many runs.

It is also useful to remember that once a pillar is filled, no goblins can sacrifice to it. They will simply stand near it. Once you have filled the blue pillar, you can focus solely on the orange pillar, then clear the blue pillar once all other enemies have been killed.

When you start damage phase, the person at the base of the tether will arrive at the other pillar first, giving them the opportunity to hit a "ground shot" on the boss. The boss becomes damageable as soon as the tether connects, but he spends some time walking around on the ground before he jumps up. It can be helpful for this player to hit their first Izanagi shot before he jumps into the air. The other player may occasionally have the opportunity to hit this shot depending on their speed, as well as the positioning of the boss and the pillars. The boss's crit spot is slightly different while he is on the ground; it only occupies about the bottom third of the white spot on his stomach. If you have the opportunity to take this shot, hitting a body shot can potentially lose a lot of damage, so be sure to hit as low on the crit spot as you can to try to make sure you get full damage.

This fight can be difficult at first, but once you get the hang of clearing enemies quickly and efficiently, surviving in the boss room, and doing good damage, it's not as difficult as it may seem. Good luck!