https://www.youtube.com/watch?v=CeAGUnsLDrE
Note: Thanks to Big_b00ty_h0e for the gameplay video. His build uses a slightly different setup than mine and he's doing low anomalies, but the way the build plays is there (he does it better than me, actually).

Hello. I'm too lazy to write a neat guide with pictures, so if anyone wants to do it or make a video or something, feel free to and I'll erase this. Also, the Demon Lord warlock probably kills stuff much faster but this build is infinity times tankier, scales with enemy HP and doesn't require any annoying gear swapping.

Here's the essential info: Rune of Reaping + Sudden Death kills everything regardless of how much HP it has, even if you do 0 damage, and kills decently fast. This means you can focus absolutely everything on being as tanky as you can and you'll still be killing stuff. This guide is just to show you how to kill trash faster.


Stuff to kill trash monsters faster and not die (aka skills and gear):

*Poison Tree: Just max every passive if you're lazy like me. The important ones are Outbreak and Infected Spirits. You don't need any active here but you could get zombies for meat shields (they're pretty decent).

*Frost Tree: Max Spirits of Vengeance and the stuff related to Soul Warp. +Mana passive is also nice, so is cooldown reduction. Frozen Veil is ok. Cold Death is useless. The crit damage passive is close to useless and you don't need any active skill other than Soul Warp (but you need to spend points for requirements, so get the less crappy stuff like slows).

*Fire Tree: You'll have 2 skill points left after you get all you need from the other trees, you can put them here for more HP and/or damage reduction.

*Shadow Tree: Put at least one point in Life Reap and Sudden Death, max Undeath, Soul Feast, Ritual of Souls, Bone Spears and its +range passive, put one point in Death Knight (ultimate) and Necrosis (last passive). The rest doesn't really matter, but Soul Eater is nice for emergency healing if you didn't get zombies (Soul Barrier isn't that strong in this build). The rest is up to you. You don't need the overpower passive, by the way.

*Masteries you don't need: Overpower, increased life/mana on hit and any form of damage increase (including plain +Damage, +Infection, +Any element type, +Curse/Bane/Sorcery, +To crowned/undead/whatever, Skill Tree Focus) all add extremely little or are useless. Critical Damage only affects Outbreak damage (maybe the epic ring enchant too) but you're not going for Crit Chance, so it's pretty useless too.

*Elemental Masteries: Get all the ones related to Spirits of Vengeance (last one in poison line, two more in frost line), Outbreak (first one in poison line), Sudden Death (first one in shadow line) all the various defensive ones in the fourth column of elemental lines (evasion, damage reduction, stagger and +healing) and Soul Jars + Frozen Soul perks in frost line. The shadow perks are nice too and maybe the Masochist one if you have it. Don't forget Ritual Affinity from one of the rightmost perk slots. Also, the poison perk that makes zombies cast Outbreak when they die if you got zombies.

*Central Masteries: Stuff from the center should be fairly obvious, except you only need +20 to all resists. You might want companion-related stuff if you went for zombies, but it's ok if they die a lot. Split the rest of the points between Mana and Health (prioritize Mana).


Gems and Gear Enchants:

*Gems for Helm/Chest/Boots: For Prismatic sockets, Star with Evasion. Then your choice between maximizing number of sockets or maximizing Evasion. If you choose the former, then +Mana% square gems on sockets that aren't Stars but go for 2 Stars and 2 Squares on chest. I think it's better than going full Stars for max Evasion.

*Gems for Amulet/Ring/Accessory: Two Star sockets with +Chance to Steal Souls. All the rest is up to you but all the options are either ♥♥♥♥ or useless. Health/Mana Regen are the only ones that help with killing stuff, by giving you a tiny bit more survivability (Mana probably better). Remember you don't need +Elemental Damage (seriously, it doesn't do anything). I went with all Pickup Radius but you could get Magic Find (or Light Radius? lol).

*Gems for Weapon/Offhand: For Prismatic sockets, Square is the most versatile for pretty much every build. Then either go with 1 Attack Speed gem + rest Cooldown Reduction, or all Cooldown Reduction.

*For Epic/Major enchants the priority is +All Resists (amulet, chest, boots, accessory and ring), then Damage Reduction (Epic, amulet and chest), then Damage Stagger (helm and offhand, chest doesn't have enough enchant slots), explode monster on death (Epic, ring only), and 1 Attack Speed enchants with 1 Attack Speed gem, 3 or 4 with full Cooldown Reduction gems (4 is a very small increase). For the rest, get Health or Mana (I think Health is better but you can mix or try full Mana).

*For Minor enchants the top priority is Cooldown Reduction and Gem Strength. Split the rest between Reach and Effect Duration where applicable (maybe prioritize reach). Get Mana Cost Reduction otherwise. You can't have any of those on Boots, so get Pickup Strength and whatever else you want.


Actual Gear:

*Weyrick's Crown (Life Guard Greater Rune). True Legendary. Or Lich's Crown (see below).
*Any Amulet with Star of the Pure power. Hellstone Amulet is probably the only other one with a power that's not garbage. Ferocity has a useful extra enchant, but the power is close to useless for this build. Amulet of Despair doesn't affect any of your main sources of damage.
*Lich's Armor (Vestige of Lost Souls Greater Rune).
*Battle Boots (Staggering Boots Rune). True Legendary.
*Heart of the Forest (Balgar's Binding Greater Rune). True Legendary. The rune comes from a berserker True Legendary accessory. Iceheart Rune might be a decent alternative with full Lich's set. In this case, I'm not sure which Greater Rune is better on helm.
*Lich's Manifesto (Jon's Book of Souls Rune).
*Lich's Wand (Lesser Rune of Reaping). The rune drops in anomalies.
*Ring of Pure Energies (Kingsrock Rune). True Legendary.
*Codex of Soul Warp (or scrolls).
*Codex of Healing Touch (optional).
*Finley's Magical Map (optional).


Keybinds:

Life Reap and Death Knight, in this order, on the same button.
Bone Spears and Soul Warp, in this order, on the same button.
Ritual of Souls on an emergency button.
Soul Eater and Codex of Healing Touch on another emergency button.
Codex of Soul Warp and Finley's Map on other buttons.


How to Play!:

Use Codex of Soul Warp (or scrolls) a bunch of times and talk to Tinka before entering an anomaly so you enter with full souls and mana.

Gather a decently sized pile of enemies (like 10 or so). Hold Life Reap button until they all explode. If you gathered more enemies than you can tank, just Life Reap around the edges of the pile a few times then hold the Soul Warp/Bone Spears button to teleport around until they get low enough for Bone Spears to kill them, then the entire pile should explode. Spirits of Vengeance will appear and start doing trillions of damage. Then you need to Soul Warp ahead of the Spirit while gathering more enemies with Bone Spears for it to kill (hold the button and you will alternate between Soul Warp and Bone Spears).

Alternatively, just go around teleporting and Life Reap/Bone Spear stuff like in the video and hope everything dies before you do.

Sometimes the Spirit will expire because the layout of the map is bad and the Spirit got stuck behind a wall somewhere, or you went in one direction and it went off in elsewhere, or you just got unlucky since there's only about a 30% chance an enemy will spawn a Spirit. But if you're fast and not too unlucky, you can unlock the next anomaly floor with just the initial Spirit. Finley's Magical Map is nice here, you can reveal the entire floor, teleport to one corner and then follow an optimal path towards the exit.

You should watch your mana bar just as much as your life/shield bar. If it goes empty you'll die really quickly. Regarding the life/shield bar, it displays your shield strength relative to your current HP. This means that if your bar is half red, half grey, you have an amount of shield left equal to your current HP, which is a VERY LOW AMOUNT. You should retreat and wait for your shield to recharge in this case.

If you need to quickly recover your mana, just quickly tap the Soul Warp button instead of holding it and you should teleport around without using Bone Spears (or just spam scrolls). The souls gained will replenish your mana.

If you're tanking monsters and you character screams that he's dying, that means you have so much staggered damage that you will most likely die. Teleport away from the monsters, cast Ritual of Souls, which will boost your max HP and make you eat the souls floating around you, then spam the Soul Eater/Codex of Healing Touch button (don't hold it, if you do then Healing Touch won't cast). If you do everything fast enough you should survive every time. If you have zombies instead of Soul Eater, cast Healing Touch and good luck.

It's fine if you die, you don't need to stack anything or do any setting up except casting Ultimate and filling your souls and shield. You can promptly go back and kill stuff.

For bosses just Life Reap until they die (takes like 5 seconds).

That's it. I hope you like reading!

EDIT: corrected something about attack speed enchants
EDIT2: added video, made some minor clarifications/additions everywhere, removed stuff about a bug that was fixed.