This post is for those of you that are still having trouble beating Skolas, with or without Giggityhorn. The key is patience. I've ran through the 35 easily with people whom have never beaten Skolas post-nerf. It just takes time and patience. I do have gjallarhorn, I use it, but I prefer not to use it on Skolas because after the bonds are broken, there are actually 5 or 6 spawn waves, not just when he's at 50% and 25%. I just use Ghorn for cleanup, which is not necessary at all.
My load out for this week consists of
Primary: fatebringer, great for grouped up enemies, and it's a 1shot for dregs and 2shot for vandals
Secondary: high capacity mag arc shotgun with high ROF, or Lord of Wolves to buff teammates. For after the enemies are dealt with, switch to a sniper, like black hammer or icebreaker
Heavy: arc machine gun, e.g. thunderlord or against all odds with field scout, something with high impact and decent magazine size.
1. Go left to take out the servitor. Once you take it out, enemies will start spawning. If you can't break his bonds, don't worry about it. Take out the enemies, go to the right, and try again. Wait until Skolas gets in your line of sight, then take his health down as much as you can. If it takes a third time, enemies may or may not spawn. If it takes a third time, head back over to the starting point traveling away from Skolas (I usually prefer to go towards the edge as it's quicker and you get more space from the melee captain that way, traveling through the halls immediately draws his attention and he follows you; this can be a hassle if you're swapping essence)
2. Once the bonds are broken, eliminate the ads. There are 2-3 captains with shrapnel launchers, and one melee captain spawning from the right. I prefer to be on the right when ads are spawning because he will stay underneath you. If you manage that, whomever has the essence should drop down with an arc shotgun and blast him. That way if he kills you, you don't have to worry about the essence for a good while and there's plenty of time to kill/draw enemies away from your corpse. Once ads are taken care of, start whittling Skolas' health down. Whomever had the essence should call out their time every 5 seconds, and there should be an order predetermined. One person should not be shooting Skolas and should be paying attention to the radar. As soon as there's activity, STOP SHOOTING SKOLAS. You will have less enemies to deal with when you are dismantling mines. If you try to melt him, you will have two waves of ads to deal with, instead of splitting them up.
3. Take out the ads. Again, I try to be on the right so I don't have to immediately keep an eye on the melee captain. You can kill enemies, get some breathing room, then drop down and take out the melee captain. If you're on the left, someone needs to scan for him. He is the bane of all existence, and he will eliminate your entire fire team FAST. If he starts destroying you all, don't be afraid to rotate. Get some space.
4. Once those ads are taken care of, go ham on Skolas until mines appear. Make sure you get a fresh change over on essence though, so you're not distracted and wind up dying while trying to dismantle mines. Everyone travels together to the first mine, especially in the middle. Takes like 5 seconds to dismantle the mine with 3 people. Get in, get out. Whoever just had the essence CAN go off on their own and it be 2:1 on the other mine spawns. Once they're taken care of, go to the side with the least amount of ads. Regroup. Start eliminating enemies.
5. Once ads are taken care of, whittle his health down again. One person should be paying attention to radar. Once activity shows up, eliminate the enemies.
6. At this point, Skolas should have very little health. Be patient. Now you go to the left side of the map. If you look towards the middle of the map, on the left there is that huge drop. Try to get him right there. Have a scout or a hand cannon equipped, and an ascended rocket launcher. Take his health down a little, equip rocket launcher, and burn the rest of his health.
The most important thing is to communicate and don't get too comfortable in one spot. When you do leave your spot, EVERYONE TRAVELS TOGETHER. If one person dips, you all dip. You will rotate a lot. If someone goes down, use your best judgement. You can hold your position a lot better on the right side on the overhang (enemies won't rush you) until you can If someone goes down on the left side(where you start the encounter with the servitor). If Skolas gets close, just rotate. It's great to have self res warlocks or at least 1 in case someone needs to pick up the essence.
I hope this helps. I will continue to update for any questions or any other tips.
Edit 1: You can add me on PS4 if you want to try it with me.
PSN: bigricharddaddy
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Here's the cliff notes: kills ads, damage skolas, repeat.