While you're in the Hall of Souls, you may notice there are 3 spire things that are located in the three main sections not including the Court of Oryx. Every now and then, a symbol will be flashing above the doors with Taken outside of them indicating that this location contains a mini boss fight complete with around 15 enemies total: 3 rounds of 3 enemies and 6 on each entrance to the section.
From my understanding, you must kill all the acolyte eyes and then ALL the other Taken enemies BEFORE you take down the Taken Major. Once you do this, it should read something along the lines of "a relic appears from the void."
^(This is what I did and it worked whereas other times when I didn't do this is the right order, it didn't work. Although, this still may have a possibility of being just RNG)
Once you get the relic, you have a 1 minutes 30 second debuff WHILE HOLDING THE RELIC to run to the hole where the chest is located, (if you're in the hall going towards the Court of Oryx, it should be the farthest section to your left across the room, which is close to the entrance that leads you to the Hull Breach) then all you have to do is wait to collect your sweet loot.
If done as quick as possible, from the farthest section (hall leading towards Court of Oryx), you should still have around 20-25 seconds left on the debuff while collecting the loot.
Side note: if you mess up in one of the three sections, wait to see which one will be next. Once you see which room, the taken will continue to spawn in that circular pattern around the whole area of the Hall of Souls
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You can also get it if you use your super before opening the chest, you will die but it will open just as you die.