Level 100 LL Crit Ball Lightning of Orbiting Inquisitor^3.25

Notes

Featuring the following items from the TFT Mirror Shop:
Grim Grip Synthesised Ruby Ring https://forbiddentrove.com/rings/
Empyrean Clasp Simplex Amulet https://forbiddentrove.com/amulets/
Glyph Lash Heavy Belt

Video showcase: https://youtu.be/yIV05643z0M

Build mechanics
Energy blade combined with Battlemage and Spellblade support gives so much flat lightning spell to any spell, that you don't even care for the base damage of the skill gem.
Strength stacking gives flat life (transformed into flat ES by Ivory tower), percent ES scaling with legacy Shaper's Touch, percent damage scaling from Iron Will and amulet shaper prefix, 
critical strike chance from Inqisitor Righteous providence, along with Rathpith shield also scaling damage and crit chance. The mana cost of your spell and the drawback of the shield is trivialized by using Blood magic + Eternal Youth keystones, 
serveral thousand life per second recharge is always up, because damage is taken from your ES. Ivory tower ES gain works best with most of your life reserved, but you want to leave 100-200 open for the mana (life) cost of your spell. 
Using Brutal Restraint Balbala timeless jewel, one flask slot is left empty to generate flask charges for Coruscating Elixir for a near 100% uptime even without killing mobs. The timeless jewel also provides Frenzy Charge generation. 
TWWT jewel provides Endurance charge generation. Physical mitigation is coming from the Armour and Energy Shield mastery on the skill tree in the form of 5% ES recovery for each physical hit taken, 
which makes tanking burst damage from swarming monsters easy. Enduring cry is used for some extra regen.

Skill gem + Tree variations:
By only swapping your main skill gems and a few jewels/nodes on the tree you can adjust the build to the choice of your skill!
I included many spells already minmaxed in this pob, you can switch between them on the top right dropdown "Loadouts", this changes the active Skill tree, and the active Skill gems, the Equipped items are the same for all loadouts!
The build can do this much DPS with the following skills: Ball lightning of Orbiting 1.6 Billion DPS, Firestorm of Meteors 1.8 Billion DPS, Bladefall 900 Million DPS, Ice nova of Frostbolts 3 Billion DPS, 
Spark 1.3Billion DPS, Penance Brand of Dissipation 1.2 Billion DPS (all of them are maximum single target DPS, not clear)
I included a "Generic Spell" skill tree which works with any spell, but you can get the most DPS by using the speclialised skill tree named the same as the Spell.

Jewel variations/crafting:
The build needs magic corrupted jewels for the legacy Adorned jewel up to 150% bonus increase.
7% increased maximum Life (Vivid) prefix and +15% to Critical Strike Multiplier for Spells (of Unmaking) suffix OR +16 to Strength suffix works on every skill. 
If you are not decided on a skill yet you can just roll these and try out every skill. If your skill is elemental you can also roll for +15% to Critical Strike Multiplier with Elemental Skill (of Elements) suffix 
or +18% to Critical Strike Multiplier with Fire/Cold/Lightning skills (Infernal/Arctic/Surging) prefix. Only Cobalt jewel base can roll all of these, check which ones you can roll if you get a Viridian/Crimson jewel base.
For synth implicit the best dps mod is 3% increased Cast Speed while holding a Shield, and best allaround is +5 to Strength which also gives defense, and +4% to global Critical Strike Multiplier is a decent mod if the other two are not available.
It is recommended to use at least one "0.2% of Spell Damage leeched as Energy Shield" mod for better recovery. If you want to use Spark then you want several jewels with 5% increased Projectile Speed.
Before rolling apply a gilded fossil implicit that you can later Vaal off for a corruption mod. Easiest way to roll is to get multiple bases then just alt spam binding clicking to scroll wheel, search for the mods you want, 
and when hitting at least 1 good mod, you annul augment until you get the second.
After hitting 2 good mods you just divine, then with Craicic Chimeral and Black Morrigan beasts you apply a Hinekora's Lock in the menagerie (not the expensive currency, the beast recipe, costing ~6+1 divine each), 
then hover with a Vaal Orb (don't click yet!) and see the result, if the result is not desired, you Blessed Orb to "reset the lock", or if the implicits cannot be changed you imprint which also "resets the lock".
For corrupted implicits you want either 4-5% increased Area of Effect, or 8-10% increased global Critical Strike Chance, or 2% increased Reservation Efficiency of Skills (check the skill trees how many of each).

Item acquisition
For a Rathpith with legacy percent strength crucible mod you can buy non-unique Titanium Spirit Shield base from this trade link: then Orb of Chance into a Rathpith with Omen of Fortune (guaranteed result, only 1 Chance Orb)
Doom Crown Hubris Circlet is owned by Captainlance9, and I (ign Markusz) service it on Standard league without a fee.
Boots craft: get an enchanted str/int base, use Hollow + Fundamental fossils until you get abyss socket + T1 str or T1 int or T1 life, fracture as a 4-mod with as few bad mods as possible, then use the same fossils to get all 3 suffixes at once, 
then apply a searing implicit (eldritch ember), and repeatedly Exalt then Eldritch Chaos/Annul the prefixes until you hit T1 life (as an only prefix), add bench mod Suffixes cannot be changed then Veiled Orb looking for MS + Onslaught, 
then bench craft hybrid life.
For your That Which Was Taken jewel you have several options: #% increased Strength, +# to Strength and Intelligence, #% chance to gain an Endurance Charge when you are Hit OR #% chance to gain an Endurance Charge when you Stun an Enemy, You and nearby Allies have +#% to Elemental Resistances, Culling Strike, Critical Strikes have Culling Strike, You and nearby Allies have +#% to Elemental Resistances, Every 4 seconds, Regenerate #% of Life over one second, Regenerate #% of Energy Shield per second, +#% chance to Suppress Spell Damage, #% chance to gain a Power Charge on Critical Strike
Required tattoos: Honoured Tattoo of the Flood (x1), Honoured Tattoo of the Sky (x11), Honoured Tattoo of the Tuatara (x28)

Skill-specific mechanics:
Each skill has its own specific ideal support gems.
For skills which can use Awakened Spell Cascade (Bladefall, Firestorm) you want to get 2 extra Intensity stacks for the Intensity support gem from the skill tree (the less AoE from it also helps because it has better chance of overlapping, 
so better chance of multiple hits). For projectile skills (Ball Lightning/Spark) you also want to get 2 extra Intensity stacks for the Pinpoint support gem (the drawback of less projectiles doesn't change Ball Lightning of Orbiting at all, 
and for Spark it doesn't really matter). 1 Intensity stack is available on the caster mastery, for the other one you have to buy a legacy area cluster jewel with the Intensify notable. 
At 5 intensity stacks with Concentrated Effect, Bladefall can hit 4 times each cast, Firestorm can hit 3 times. AoE skills which can use Intensity also have great clear while moving and naturally switch to single target if you stand still casting, 
no need to press another button.
Firestorm of Meteors is better than the other two versions when using spell cascade and spell echo because the maximum firestorm count doesnt affect it.
Ball lightning of Orbiting with decent AoE investment hits 13 times in the center. Slower projectiles on it not only increases the damage, but makes it easier for the projectile to hit during all of its duration.
Reap in the correct overlapping spot hits 3 times with Awakened Spell Cascade.

If you picked your own skill check if you can use the above mentioned supports, pick the skill tree for it that is closest to that skill, and see which jewel modifiers you can use. That's it, you can achieve a minmaxed version with a few adjustments.
For any skill always check your Critical Strike Chance in game once you geared up, and if you are not at 100%, you can either get more on jewel corrupted implicits, getting more Intelligence either by not tattooing over int nodes, 
or getting hybrid Str+Int jewel suffixes, or getting a Watcher's Eye with Wrath and Zealotry critical strike chance.
It is possible to optimize the skill tree further with a Keystone tattoo, getting Pain attunement or Iron will at a closer location, saving a few skill points.

Full DPS version
If you are not concerned for defenses and just want peak DPS for a situation, you can swap in legacy Atziri's Promise flask, a Sulphur flask with legacy 17% cast speed suffix, Lethal Pride timeless jewel with Double damage modifiers, 
enough regen and max fire resist to sustain Righteous Fire, and a few changes on the skill tree for 5+ Billion DPS on Ice Nova of frostbolts.