Shroud of the Apocrea is an event that comes back a few times a year. The event is difficult and typically done in parties due to the difficulty of the event level itself along with the fiend/undead arenas that can also be selected. I have been farming Apocrea solo for a few years now and have settled on a loadout that serves me well in any of the levels that are selected.

Please note that I will only be listing my specific set (along with cheaper/easily obtained alternatives) that I use for Apocrea. I will explain my choices as well.

Armor Recommendations

Overall, I use one loadout for any of the levels. One cannot afford to change the equipment due to the importance of the loadout for farming sigils in plateaus. This guide is primarily focused on the plateaus without taking the arenas into account. If you wish to only farm the arenas for radiants, crowns and heat and generally skip the plateaus, please refer to the fiend/undead arena guide and feel free to change your equipment.

Please note that I am listing my loadout but am also listing cheaper alternatives as my primary loadout uses non-readily-available equipment.

Helmet & Armor Choices
I personally use the black kat cowl and black kat raiment due to the shadow/normal defenses and freeze resistance. Both pieces also have a universal damage bonus (i.e. the damage bonus is applied to any weapon type, not just swords or guns) and a move speed increase of low for each piece. Go faster, resist damage from most sources in the mission, resist the freeze monsters on plateaus and instantly have a damage increase of maximum? Can't say no to that!
Alternatives: A cheaper and readily available alternative set is the dread skelly mask and dread skelly suit as they have the same defenses/resistances along with poison resistance but lacks the universal damage bonus and move speed increase. Another alternative that is not as readily available is the snarbolax cap and coat, having the same defenses and resistances as dread skelly but has a sword damage bonus medium per piece as well.
Unique Variant Recommendations: I would primarily aim for status resistances of any kind if you are using a black kat set to compensate for the debuffs for the arenas that you may encounter should you decide to do them, namely fire, shock or poison. The main threat on Grasping Plateaus, the Apocrean Harvester, deals non-typed damage so any defense increases will not help on those levels. If you are using a dread skelly set or snarbolax set, I would aim for a freeze or poison unique variant to stack on your existing resistance.

Shield Choices
My choice for shield is the gorgomega, hands down. High normal/shadow defense, high health, freeze resistance, what more can you ask for? Admittedly, it has a move speed decrease of low but this is easily negated by using a black kat piece, otherwise it is a bit of a hinderance without compensation.
Alternatives: Alternatives can be found in the dread skelly shield as it has the proper defense and resistances for the grasping plateau. The only downfall is that, while the stats are technically the same, the dread skelly shield takes far less hits to break than the gorgomega. Otherwise, the dread skelly shield is perfect for the mission.
Unique Variant Recommendation: Unlike the variants for the armor, I would recommend variants in shadow defense so it can take even more hits from typed damage sources in the plateau, like scarabs and bombies. A normal defense variant would be alright as well. This would apply for both the gorgomega and dread skelly shield.

Weapon Choices

Please note that while it is possible to skip on two weapons of this loadout, I highly recommend investing in two weapon slots as all these weapons have their use. If you really cannot afford two weapon slots and still want to try and solo it, take the divine avenger and electron vortex/alternative to the vortex.

First Weapon: Combuster/Glacius
The combuster's fire inflicts more damage on the souls is you can charge for it. The glacius' freeze is also helpful as it will keep souls in place so you can charge again and hopefully freezelock it. Personally, I only use the basic attacks for my combuster in case I can swat at a soul quickly if they're close for a finishing hit.
Alternatives: You can use the Voltedge too if you want but it's not a huge deal.
Unique Variant Recommendations:: Charge time reduction variants of any kind will stack on the level 10 heat bonus of charge time reduction medium. Charging is gud!

Second Weapon: Divine Avenger
Similar to the undead/fiend arenas, this weapon is once again my bread and butter to soloing Apocrea. After using an electron vortex on a breakable gravestone, the divine avenger's wide swing and high damage will allow you to deal with the scarabs or souls that spawn. Scarabs can be killed in a max of three successful swings with the divine avenger. The souls can be killed in a max of four successive swings. Since they will be swirling around in the vortex, they are effectively sitting ducks for a short time and will also take damage when the vortex explodes, which could finish off your targets.
Alternatives: I really can't recommend alternatives here. It's essential to this loadout. If you have suggestions, feel free to post!
Unique Variant Recommendations: Attack Speed Increase of any kind is super helpful.

Third Weapon: Electron Vortex
This amazing bomb pulled my soloing loadout together after using a shivermist buster for a while. Simply plant the bomb next to a breakable gravestone. The first explosion will break the stone and swirl anything that spawns in it around for a while before exploding and potentially inflicting shock. The shock from the exploding vortex is amazing at interrupting a soul's movements so you can catch up and finish it off. However, be careful as a shocked soul that floats too close to another breakable gravestone can break it and potentially unleash more souls! The electron vortex deals elemental damage, which will deal extra damage to scarabs and bombies.
Alternatives: The Graviton Vortex is a Basil-obtainable line that is very similar to the electron vortex. However, it deals shadow damage (which scarabs and bombies resist) and does not inflict any status effects on the second explosion. While it isn't as useful as the electron vortex due to the lack of shock and the shadow damage, the overall tool of keeping enemies in one place is the most valuable part and makes this bomb viable.
Unique Variant Recommendations: Charge Time Reduction of any kind is key. I will highly recommend that your bomb be level 10 simply for the charge time reduction heat bonus. The more charge time reduction you have, the faster you can plop them next to gravestones, the faster you can finish your plateau.

Fourth Weapon: Arcana
Arcana is a little gem of a gun. I was so thrilled when they released it during the gunner update. Before Arcana, I used the Argent Peacemaker, of which I wasn't too happy about since its hitboxes are a bit wonky. It is a super useful utility in being able to snipe souls from afar if they're floating too far away from you to be able to use a sword. Its damage is high enough that it deals a decent bit and can pick off a soul relatively easily in a few shots.
Alternatives: The Argent Peacemaker is a decent alternative, though I certainly don't prefer it as it takes more shots to deal a decent amount of damage and as I said earlier, it has a rather odd hitbox. I would recommend against using any kinds of alchemers as the angled shot could hit another breakable gravestone and potentially release more souls or enemies. A lot of people also like using the blitz needle and charging the shot against souls that are frozen or stuck in a vortex. This could be useful too though I personally prefer to use the divine avenger.
Unique Variant Recommendations: Attack Speed Increase on either the Arcana or Argent Peacemaker is always a plus.

Battle Sprite Choices
The maskeraith is my go-to emergency save if things go wrong in a plateau. When I say things go wrong, I mean the Apocrean Harvester has teleported onto your head (YES, he can do that!) and is now attacking you and you have precious little time to run away. In this circumstance, one can attempt to dodge the arms trying to grab you but if you are caught, you can simply cloak and he will lose his aggro on you. Or, if you don't feel like dodging his shenanigans, you can just cloak and shield and he will ignore you, the line of arms going in a random direction. This works well in parties too but he will despawn if you are going solo. The cloak lasts about as long as the arms do so if you cloak just after being caught, you will be freed just before the cloak ends if you have a fully upgraded maskeraith cloak.
Alternatives: A drakon is a decent alternative to the maskeraith but only if it has its ultimate skill in Flame Barrier and the ultimate chosen is Backfire Barrier. If the Apocrean Harvester teleports on your head, you can simply pick a direction to run, use Backfire Barrier and outrun the arms with relative ease. However, if you aren't fast enough, you can still be caught and will be forced to shield to reduce the damage as the harvester uses its gaze attack. Then, you still have to evade him once more as he starts attacking again.
Recommended Pet Perk: Bomb Charge Time Reduction. If you have a decent charge time reduction variant on your vortex bomb, you could swap this out for sword attack speed increase or move speed increase.

The Grasping Plateau: Information

The Grasping Plateau is a MASSIVE, rectangular shaped graveyard. The moment you enter the graveyard, you will have a map that is only static and showing you no details of the area. There is a glitch where if you have connection problems for a short time while loading in, you may end up having the map but it is rare. Here is an example of a map that was glitched and appeared for a player to get an idea of the shape of the level. The elevator, golden keys and golden gates will show up on the static map when you get close to them. I like using these landmarks as a general idea of where I might be as their icon will get smaller if you are farther away. I have found they tend to like to spawn on one end of the map or the other so I'll go to the other end of the map and work my way towards it to save time. There will be 1 or 2 puzzles on the map. If you solve them, you will be given 18 sigils and potentially an obsidian shard or binding essence. The various kinds of puzzles can be found on this page where there are screenshots of each puzzle's two corresponding areas.

The main enemy you will encounter is the Apocrean Harvester. This baddie will harass you relentlessly until you stand on the elevator or leave the level. His first attack will trigger if you get too close to him. He will start to raise his arms in the air and after a few seconds, will thrust them into the ground, causing many arms to come out of the ground and try to grab you. Your shield can take a couple hits from the arms but can break very quickly and still result in being stuck. If they succeed in grabbing you, you will be unable to move or turn but can still attack. His second attack will trigger once he is close enough to you and you are stuck. He will use a gaze attack that appears to suck souls out of you while dealing heavy damage. You can reduce the damage by shielding, assuming you have an unbroken shield. You will be released and he will then start his first attack again, allowing you time to run away again.
The best way to handle the Apocrean Harvester while you are soloing the plateau is to use your dash. Dashing causes him to lose aggro just long enough to despawn. Even if you dash close to him by accident, provided you dash before he attacks, he will despawn before his attack finishes. Provided you dash often, every 10 or so seconds, he won't be a major problem.
The Apocrean Harvester can be a total butthead sometimes. On occasion, he'll end up spawning on TOP of your head!! It'll startle you, it'll make you freak out and it'll make you run away. Or, if you let him get too close and are unable to dash in time to cause him to despawn, you'll have to handle him another way. If you don't have your drakon's Backfire Barrier ready or your maskeraith's cloak ready, and/or you don't want to lose your place on the map, you'll just have to evade the arms. The best way to do this is to run directly away from the harvester in any direction for a short time. Then, turn at a right angle and run in that direction for a short time. Then, run back towards the harvester for a very short time and the arms will be unable to turn fast enough to get close. By this time, you should be able to dash again to lose his aggro and cause him to despawn safely. Only dash once he is done starting his arm attack and is moving towards you again.

The Grasping Plateau: The Gravestones

There will be columns upon columns of breakable gravestones in the plateaus. These are where you get your primary source of loot! These gravestones are easily noticeable with glowing green cracks on them. Your loadout is designed to drop a single vortex bomb right next to each gravestone. The first explosion of the bomb will break the gravestone and trigger the vortex. Whatever is inside, if anything, will swirl around in the vortex for a short time before a second explosion sends them flying! If using the electron vortex, there is a chance that a monster that spawned from the gravestone will be inflicted with shock. If inflicted with shock, they will stay put during the 2nd explosion.

3 different kinds of monsters can be found inside breakable gravestones. There is a chance, on breaking a gravestone with any attack, that you will find nothing, find freeze themed bombies, freeze themed scarabs or apocrean souls.

Bombies are very easy to handle. Upon breaking a stone with a vortex, the bombies will be caught in the vortex, unable to run around. Simply move in close then run away immediately so you are diagonal to them. They will detonate safely with you out of the way of their explosion and bullets. Keep an eye on their bullets, however, as they can break breakable gravestones and potentially release more bombies, scarabs or souls.

Scarabs will also be caught in the vortex on the bomb's first detonation. Take out your divine avenger and approach the scarabs. They should be attacking in the direction you were standing relative to their location. Do not approach them in the direction they are attacking or you will take damage. Approach them from one side and swing your divine avenger twice in succession and you should kill most if not all of the scarabs. You can pick off the rest with your combuster/glacius, divine avenger or arcana.

Souls are harmless little fellas who just want to be free! The moment you realize there are souls in the vortex, pull out your divine avenger and swing as quickly as you can to deal as much damage as you can. If you're lucky, you'll deal enough damage that the vortex's second explosion will finish them off and reward you with a varying amount of apocrean sigils depending on your tier and party difficulty. If the souls are not defeated by the second explosion and a couple of divine avenger swings, they should be left with only a little HP so they can be easily defeated with a couple arcana shots or a single combuster basic swing. Otherwise, you may need to chase them down a little, which is where the arcana really shines. You will want to defeat these souls as quickly as possible. After 30-45 seconds, if they are not defeated, they will disappear and you will not get any sigils from them. Their movement is very erratic, hence my strategy of using a vortex to keep them in place for a while and deal as much damage as possible, if not take them out completely before they can float away.

The Grasping Plateau: Strategy

Upon loading into a grasping plateau, you will find yourself on a random part of the map. Your map should be static and you'll no doubt see many breakable gravestones scattered about various structures and nonbreakable gravestones. It is a foggy place and it can be difficult to see a reasonable distance.

The first thing I do when loading in to a plateau is move either left or right until I find the edge of the map. The edge of the map is characterized by a long, winding barrier. The corners of the map have a tall structure that has candles on both sides facing vertically and horizontally. In general, I'll try to find a corner of the map, sometimes breaking gravestones along the way with my vortex and dealing with whatever spawns, if anything.

Think of the grasping plateau as a massive grid with the gravestones spawning in one square of the grid. Sometimes, gravestones will be missing in their individual squares but you can keep track by the other gravestones around it so you can keep count. Once in a corner of the map, I will start clearing gravestones by going up and down along the map. I will clear 4 columns of gravestones in one pass, keeping track by noting which column a breakable gravestone is in by telling myself in my head. (Add a screenshot for clarification as this is no doubt confusing!) Once I reach the top or bottom of a column, I will move four gravestones over and start going vertically once more. I'll repeat this pattern until the entire plateau is completed. On one end of the plateau, you will find that you have 2 extra columns of gravestones, I generally will clear a single section of 6 that when I first start a plateau so when I reach the other end, I have only a column of 4 to do. (another screenshot to clarify)

Tips
Keeping track of where you are can be troublesome at times, especially if you have a runaway soul. If you can't remember which column is which number, don't hesitate to run back to an edge of the map (don't forget that there's an extra 2 columns!) and count groups of 4 columns until you are back where you lost count.

A fantastic way to keep track of where you are is using a golden key as a marker. A cat statue can also be used but it isn't seen on the static map. Simply put the golden key where your 4th column is. When you return to the same side your key is on, you will be able to move your key 8 columns over to mark your next 4 columns to clear. (screenshots to clarify)

If this whole column/grid system is confusing to you, that's okay, it's rather hard to explain! You can still clear the graveyard by going up and down along one side of the graveyard, clearing stones as you go without keeping track of where you are. Be careful to not go too far over at once so you don't miss gravestones!

If you come across a puzzle that isn't marked on the map and you have no icons such as golden gates or elevators to give you an idea to its relative location, you can use a golden key (if you have one) to mark the place until you find the solution for it, then take your golden key and finish your second puzzle or resume using it as a column marker.

It may be tempting to spend your sigils on materials as soon as you get enough sigils but hold off until you're done grinding sigils for the event. You may get obsidian shards or binding essences from puzzles, which will save you some time and grinding!

The Grasping Plateau: The Loot
Generally, you'll earn 300-350 sigils per completely cleared grasping plateau.

There are four different things you can obtain using apocrean sigils. There are three weapons you can craft with obsidian materials, which are bought with apocrean sigils. You will need 6 obsidian shards, 4 binding essences and 2 perplexing elements to craft a single obsidian weapon. You will need 1470 apocrean sigils to have enough sigils to buy all the materials necessary for one obsidian weapon.
The Obsidian Edge is a variant of the Acheron. It is a shadow dealing sword that sounds like a Gran Faust upon swinging. Its charge similar to the acheron's except it inflicts poison on the charge bursts. It also unleashes many tendrils as an animation.
The Obsidian Carbine is a variant of Sentenza. It is a shadow dealing gun with a unique firing sound. It fires 6 shots per clip. It is capable of poison on regular shot, making it very unique, but also poisons on charge attack. Its charge attack is similar to the sentenza except for the tendril animation on the final shot and the poison infliction.
The Obsidian Crusher is a variant of the graviton vortex. It is a shadow dealing bomb that functions identically to the graviton vortex, except for the tendril animation as well as a chance of inflicting poison on the second explosion.

To obtain all three weapons in one Apocrean event, you will need 4,410 sigils.

The one item you can get directly with apocrean sigils is the grasping aura which costs 10,000 apocrean sigils.

If you wish to obtain all four unique items from the Apocrean event, you will need 14,410 sigils. At approximately 300-350 sigils per plateau, you will need to do a lot of Grasping Plateaus!

So...are the weapons worth it?
Cue personal opinion section!!
Yes. A fair amount of people disregard them due to the difficulty in obtaining the sigils for them and the amount of grinding required. Others feel the poison effects aren't worth the work. Still others, albeit reasonable, state that the obsidian edge is not worth getting simply because of the acheron's major damage. However, we all know the acheron is broken (it appears to be pulling its damage values from the gran faust's damage table) and I expect it will be fixed at some point. That and sometimes, it's fun to not use an overpowered weapon! :P

Poison has its place too and is a very useful status. It renders silkwings and gremlin menders useless to their allies as they will actually damage their target instead of heal it. Poison also cuts down the attack and defenses of the poisoned target down to 1/3rd. You'll be able to kill your enemies MUCH faster and take far less damage if your enemy is poisoned. Of course, poison cannot be inflicted on poison themed enemies along with a few certain monsters.

Given some time and effort, you can craft an obsidian weapon (edge's precursor is silent nightblade, carbine's precursor is blackhawk, crusher's vortex is graviton bomb) by having its precursor heated to level 10, one set of obsidian mats (note above for how many of each and how many sigils it costs) and the following materials: 40 dark shards, 10 vile seals and the following materials, depending on which obsidian weapon you are crafting: 8 swordstones for edge, 8 grave soil for carbine or 8 sinful brews for crusher. You will craft your obsidian weapon at the mysterious alchemy machine, which can be found in the Arcade of Haven on the far right side near the Garrison's door. Go north of the Town Square to find the Arcade and go right.

I hope this guide was helpful for you! If you have any questions, comments or suggestions, feel free to post!