Level 100 Hybrid MoM Arc Champion^3.21

Notes

LEVELING
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The early leveling setups included in the "Tree" and "Skills" section are the ones I used, but I'm no expert on efficient leveling. 
Going with the passive progression I have provided will limit the number of respec points you'll need, though.

DPS in POB:
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The DPS is not calculated correctly in POB since it goes off cast speed rather than on the trigger rate of Kitava's Thirst.

For lightning conduit, this overestimates the DPS. For Arc, it underestimates the DPS.

With the Frenzy + Prismatic Burst setup, the average trigger chance on Kitava's Thirst goes up to 62.5%.

Because of the cooldown on Prismatic Burst, we only have it available every other swing, otherwise the effective trigger chance would be 75%.
In practice, though, during normal mapping it'll feel closer to 75% if you kill packs with one trigger, since the cooldown for Prismatic Burst will have elapsed by the time you move on to the next pack.

The rate limiting factor in triggering Kitava's Thirst is Storm Cascade's cooldown (0.25 seconds, or more accurately 0.264 seconds when factoring in server tick rate).

The maximum trigger rate of Storm Cascade with no cooldown recovery would be at 3.78 attacks per second. 

Exceeding that attack speed will cause you to miss the ideal windows to trigger Storm Cascade, causing you to miss potential Kitava's Thirst triggers, which would then end up reducing  your damage.

Controlling attack speed can be done through the Faster Attacks support by limiting how much you level it up or add quality to it.

(3.78)(0.625) = 2.36 triggers per second on average with ideal attack speed.

Another factor that limits DPS is the fact that Lightning Conduit's cast time is added to its cooldown when triggered. 
The amount of cast speed needed to bring the cast time low enough to potentially trigger Lightning Conduit with every attack was more than I could figure out how to fit in the build.

Overall, when the damage of all skills are factored in, the full DPS feels somewhere around 2 million.

CONTROL LAYOUT:
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Since this build uses a bunch of buttons, the control layout you use makes a huge difference in whether it'll feel good to play.
You can check out the build video for how I set up my controls on mouse and keyboard. Xbox controller can work well, too, but I'm not a fan of inventory management using the controller.

GEAR, GEMS, FLASKS, JEWELS:
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Swapping to the build at 62 will require The Surging/Rippling Thoughts and Kitava's Thirst. Until you level up and get more mana, Atziri's Foible and Dream Fragments can carry you.
I used Ghostwrithe for my leveling chest, but other options would probably work.

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For the build to function, make sure that Storm Cascade cost is AT LEAST 100 mana.
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You can adjust Storm Cascade's cost by controlling how much unreserved mana you have or which specific support gems you have in The Surging Thoughts. 
Fine tuning can also be done by limiting the levels on your Clarity and Vitality gems to reduce/increase their flat mana reservation.

The price estimates below are based on when I purchased the items mid-league. Late league prices will probably be different and availability of some of the corruptions will be limited.
The double corruptions are icing, though. The build will function without them. You'll just sacrifice damage.

Kitava's Thirst (double corrupted) = 25-50c | (single corruption, +2 socketed lightning gems) = 10-20c 
Bench craft 4 sockets, 4 links, and recolor to 4 blue sockets using the "at least one blue socket" craft, cost will be approximately 20-40 vaal orbs depending on how lucky you get with the recolor.
If you can't find a corrupted Kitava's Thirst, you can buy up the uncorrupted bases at 1c and try vaaling them yourself. 

Singularity = 1c
High spell lightning damage is what to aim for here. The cast speed can help us, too, with faster Divine Blessing: Zealotry and Vaal Arc casts.

The Surging Thoughts = 30-40c (the market is small on this item, and I was probably driving up the price single-handedly by trying to put a good Crucible tree on one)
You can also use The Rippling Thoughts instead. It'll be cheaper. 
The cheapest route would be to buy up the first, second, and third "Piece of the Arcane Legion Sword Piece" and arrange them yourself in the inventory to create The Rippling Thoughts.  
Then, you can upgrade The Rippling Thoughts with an "Electroshock Scroll" to get The Surging Thoughts.
If you use The Rippling Thoughts, you'll just be missing out on some lightning penetration and shock chance from the Greater Harbinger Buff. Not too big of a deal.
The other stats on the sword are the same as the upgraded version.

Anathema (corrupted with "Grants Level 21 Wrath Skill") = 50c
You can use an uncorrupted version, but you'll have to drop a skill somewhere to fit in the Wrath gem. This build has a lot of gem socket pressure. 
You could drop Frostshield/Sigil of Power or Arcane Cloak to fit in Wrath. 

Mark of Submission = 1c
I slot in Divergent Conductivity (10-20c) here. If you're having survivability issues as you're leveling, you can slot in Enfeeble here instead (or put it in as the curse you use in the Hextouch setup). 
Enfeeble will make a huge difference to your tankiness.

Burden of Truth = 10c
Try to get one with "Gain 10% of maximum life and extra maximum energy shield". When you use tempering catalysts on it, you'll be able to get the full benefit with an extra +2%.

Aul's Uprising (Wrath) = 100-200c
Annoint with Spirit Void for attack damage leeched as mana. This will help with single target mana sustain. If you can get mana leech elsewhere, you could replace the annoint here for something else.

Atziri's Splendour (high ES version) = 10-20c (buy 2 of then, can start with a 4- or 5-link while you work on using fusings to get a 6L)
Sort the trade results by energy shield. Aim for one with 600+ ES.
A 6L for the chest is not required. You can manage on a 5L (4L even if you're low on fusings). The 6L lets you link Flicker Strike to the same setup as Frenzy. 
You can keep Flicker Strike unlinked, though, if you're having trouble 6 linking the chest.

Algor Mortis (Temporal Chains on hit corruption) = 10c, (temp chains/+1 frenzy) = 40-100c 
If you're having trouble finding the double corruption, I recommend getting temporal chains here over the +1 frenzy charge. Slowing enemies helps survivability tremendously.
As with Kitava's Thirst, the uncorrupted base is 1c. So, you could try vaaling some yourself to get the corruption.
Socket and recolor with the crafting bench. I go for 3 blue, 1 green.

March of the Legion (corrupted, +2 duration) = 30-50c
Good double corruptions here get pretty expensive. +2 duration gems is good enough, though. 

Watcher's Eye (% chance to recover 10% of mana while affected by Clarity + Lightning penetration while affected by Wrath + 3rd mod choice) = 200-400c
Getting the "% chance to recover 10% of mana while affected by Clarity" is the main mod you want to get here. 
I added lightning pen for a bit more damage, and I chose "% damage leeched as life while affected by Vitality" for more survivability. But, these mods are flexible based on what you can find on trade.

Thread of Hope (medium) = 20c
Medium ring threads are pretty cheap. I decided to get one with Corrupted Blood immunity, but this can definitely go on another jewel.
Until you get the Thread of Hope, you won't have enough passives to be able to expand out for the cluster jewel set up for the endgame configuration.

Unnatural Instinct (totally optional) = 500-600c
You could use a different jewel here. I had already spent a bunch of currency testing out different versions of the build, so I thought, "Why not splurge here?". 
There might even be a better jewel choice, though. You can certainly use this slot to patch up stats or resists as need. 
I aimed for at least "30% reduced effect of shock on you" on a jewel to couple with the Soul of Garukhan pantheon ("60% reduced effect of shock on you").

Lethal Pride (Timeless Jewel) = ~200c
I aim for getting "% chance to deal double damage" on the notables below the duelist start area. "% damage taken as fire damage" is also useful for suvivability. 
Fire resist doesn't hurt, either, to help cap resists.
You can use the "Find Timeless Jewel" feature on the "Tree" tab in POB to find seed numbers to search for on trade.

Awakened Added Lightning Damage = 15c
Leveling this up to 5 will give you +1 to level of supported lightning skill gems. 

Awakened Lightning Penetration = 10-15c
Leveling this up to 5 will give 10% chance to inflict lightning exposure. 
Until you have lightning exposure, don't bother taking the Elemental Mastery that gives "Exposure you inflict applies at least -18% to the affected resistance"

Divergent Frenzy = 10-20c
After getting/buying the gem, you can de-level the gem by vendoring to a merchant along with a scouring orb. I de-level it until it's usuable based on my dexterity.

Divergent Flicker Strike = ~30c
Divergent quality if not needed, but it's nice to have the increased teleport range. Same as with Divergent Frenzy, de-level this as needed.

Atziri's Promise = 3-5c
Craft "used when you hit a rare or unique enemy" through the bench so you don't have to worry about managing this flask. 
I used this flask to try to squeeze out a little more damage, but the chaos resistance is also quite nice.

Flasks = crafted

Cluster jewels = crafted, variable cost
You can use reforge chaos (yellow harvest lifeforce) on a chaos resist small cluster (3 passives). 
For the lightning damage cluster (8 passives), you can use reforge lightning (blue harvest lifeforce) until you get one that covers what you're missing (stat- or resist-wise). 
Bases are ~10c each (aim for ilvl 84 to potentially get the 35% increased effect mod). 
The three clusters I went with are increased lightning damage, non-damaging ailments, and chaos resistance.

Estimated total cost (without Unnatural Instinct) = ~700-1200c, or about 5-6 div
Estimated total cost (with Unnatural Instinct) = ~1200-1700c, or about 7-9 div