I will release this pretty early, and keep adding to it, as I improve upon things.
Ideally, this will end up as a high-level discussion about various aspects of the build and the mechanics used.
I hate testing in Martyr and avoid it mostly, so there is the possibility that there are parts of the build that are plain wrong. I'm happy to be proven wrong, don't hesitate to comment here or reach out via Discord.
If you would like to translate the guide to another language, I'm all for it and will help if I can.

I used the TA build for the ladder race in season five (and placed 4th).
I'm currently favoring the Crusader variant, after discovering that teleport doesn't break the channel, which solves almost all of the issues I had in past seasons with spin2win builds.

There are probably Berserk-variants that work equally well, or better. But I don't enjoy having to worry about token generation. Don't ask about it, i'm not going to respond. You can however try to ask for Berserk gear on Discord, I usually keep really good pieces to give away.

Both the TA and the Crusader have the damage and sustain to do missions at +50 difficulty, where the player's damage is reduced by 99%, and monsters deal 90 times as much damage.

The Crusader spin2win gear is shown here: Timestamped Youtube Vid

The 'auras' in Martyr tick very fast, so they are the ideal means to apply debuffs to enemies.

The following discusses how I build a spin2win crusader, but the general principle stays the same. I'll be adding sections for other classes and variants.

We run shock aura (available as archeotech enchant on belts, eye implants and main implants).
We run fear aura (available as relic enchant on belts, purity seals and inoculators).
We run heat aura (a four slot psalm code doctrine).
Our crits inflict bleed (purity seal of trauma, relic weapon enchant, relic belt enchant, relic main implant).
Bleeding enemies are slowed (passive skill node in DoT tree).

With the two shock-related psalm-doctrines equipped (three and six slots), anything we - or our aura - touch gets shocked and explodes, and shocks in the area, and debuffs and applies vulnerabilities.
This is what an elite looks like a split second after the auras start touching them. Also note the insane amount of overlapping 'shock resisted' messages that showcase just how fast the game tries to apply the debuffs:



Of course we use a mix of perks and passives and item stats to apply the vulnerabilities even faster, and then we roll vulnerability effectiveness wherever possible.

The next building block in ramping up the damage considerably is critical hit (chance), critical hit strength and critical damage.
We are soft-capped (50%) on crit chance through items and passives. Then we have "+5% Supreme Critical Hit Chance and +10 Critical Hit Strength against Slowed, Shocked, Stunned targets" rolled on three gear pieces, and the cherry on top is a four yellow component inoculator that is set to four Frenzon (10 Supreme crit chance and 40 crit strength). So when the inoculator is active, we are sitting at 100% crit chance and about 200 crit strength (above the magic 150 for the strongest crits).

(The 'supreme crit against' is not shown in the char screen, since it's applied conditionally)


Now, you'd think that the inoculator lasts only five seconds but has a 60 second cooldown, what good is that? Inoculators have two 'magic' secondaries, and we intentionally used the 'reroll all' feature on our gear to get the desired amount of primaries and secondaries:

6.0% to 10.0% chance to reset Inoculator Cooldown on Kill

Champion and Elite enemies have a +15% chance to drop a Supply Charge

The first one allows us to use the inoculator (with inoculator charges dropping from destructible quite often) quite liberally - at the very least we always have it available as a damage boost when fighting elites - and the latter helps us replenish teleporter charges. Just watch the cooldown refresh in my videos.
Since we are maxed out on crit chance and crit strength, 'Critical Damage' becomes the next multiplier for our damage output, that's why that is rolled on gear pieces instead of crit strength.

The next multiplicative (most damage increases in Martyr are only additive) damage boost comes from 'damage against X'.

We have
10% against bleeding (Physical passive tree)
10% against slowed (Debuff tree)
19% against bleeding (secondary on the neural)
16% against slowed, stunned, shocked (secondary on the eye)
17% against slowed, stunned, shocked (secondary on the main)
19% against bleeding (purity seal of trauma)
18% against slowed, stunned, shocked (secondary on the armor)

and on top of that, we have several hundred percent additive damage bonus, with a big chunk from the enrage tokens (440% there) and from various passives, mainly the 'center' points of the Crit tree, the DoT tree and the Debuff tree.

We want MS everywhere.

Unless I'm doing -99% missions in coop, I always have the perk 'Stride of the Blessed' active. On missions where damage could be and issue, and the missing damage reduction a liability, I switch it out for Persistent Attrition.
Edit: Feint Mastery is probably a bigger damage buff than Persistent Attrition, according to DeeezNutzs most excellent sword and board crusader guide. If you are into S/B, go check out this guide, it's very well-written and I think he tested extensively. Sword and Board Crusader
I had planned on presenting a S/B variant within the scope of this guide as well, with triple mobility skills - teleporter, shield charge and assault jump - but I found the movement to be clunky, extremely unreliable in coop, and - last but not least - Mr. Nutzs had already put together that excellent resource for it.

Morality weapons are not an option for spin2win, since red greatswords with enhanced Spinning Blow not only benefit from cooldown reduction (very important for 'spinning up' again, after stopping to use shrines or cogitators), but also lose the MS penalty that non-enhanced spinning blow has.

While in combat, we generate extra MS via perks, and get the biggest boost from triggering Thunderbolt of Authority, which grants a big supreme movement speed bonus. This is what I get during missions:



Apart from regular movement, we have assault jump from the armor, and teleport from the belt. Teleport can be used while channeling, but has some issues clearing height differences, and does not give us the 'impact' splash damage of Assault jump. A perfect example when I use the 'stomp' is after triggering Judgement Shrines.

Both abilities can be used to clear gaps in levels, the 'outcrops' on island maps and the silly inclined walkways on the big platform maps.

The best defense is of course a good offense, that's why we play super aggressively, actively teleporting or assault jumping into the biggest clusters of enemies, and life and shield draining like a mad lad.
However, we have to survive random one-shots, and that's why we actually build quite defensively.

Note: I completed the Puritan Morality bar very recently and switched to a 'Invulnerability on Kill for 2 seconds (8 seconds cooldown)' armor. I still have to test the limits of that, until I know them, I'm sticking with the defense that has been working well for me:

Completed defense passive tree, with just a couple of useless side branches left out.
A couple of points in the health tree, namely the ones that generate suppression and health, and the passive the provides suppression damage reduction.

The latter is a key part of our defenses, you need to roll it on a couple of items. It makes a huge difference. The TA with 20% of that constantly gets CCed, with 55% the suppression bar never ever moves out of the green.

The gear is somewhat flexible, but most pieces are set:.

• Purity seal of Trauma is a given. If you have issues finding one, just ask on Discord.
  
• Neural implant is the generator for enrage tokens. If you like hot-swapping, you can.
  
• Eye implant, the seasonal seems to be really good. If I'd want to use something different, I'd probably use an ancient relic 'of Stride'.
  
• Main implant: Typically the spot for shock enrage. If you can't get your hands on a seasonal teleporter (they are incredibly rare), you can also use the belt slot for shock enrage, those drop with some frequency for me, and can be crafted.
  
• Inoculator is typically where the fear aura resides.
  
• Armor: The biggest flex spot. Some ancients (like 'of Concussion') work well, Morality gear has some solid choices, and if you take a relic or archeotech one, you can add a fair bit of extra defense with reduction and allres rolls.
  
• The greatsword needs to be red, and with enhanced spinning blow. Ideally with six slots, two of which are life and shield drain, one crit chance, one crit strength, and you probably want the last one to be vulnerability effectiveness.
  
• Signums are a red general vulnerability and a relic +14 damage per Enrage token

I usually put a weapon with 50/50 loot quality and quantity in the 2nd slot, and two 25/25 signums as well, and swap into the 2nd slot before I take the teleporter to the chest room in void crusades.

Here's a snapshot of what I'm currently using. Note that this is always a little bit in flux, as new facts are established. Right now - for example - Schalimah is doing a series of tests about vulnerability effectiveness, and I just changed weapon rolls according to his findings. Some of the gear pieces I consider temporary aren't rolled to perfection, even though I play a lot, my resources for re-rolling are also finite.
The arecheotech enchant on the Greatsword is not what I'd choose if I had a choice, but that was simply the highest level, six-enchant GS I had.

early version, pre-morality gear: +18 supreme in 22 seconds Youtube Vid

Ordos intel at +17 from today: Youtube

So the thoughts (and results of my game-testing) about Tech-Adept are the following:

• We need mobility. So badly that we'll sacrifice a summoning slot from the belt for it gladly.
  
• Constructs can never compete with the damage output of the vuln/explosion 'engine', so we will remove almost all passive points from them and just give them enough so that they gain some survivability, and help debuffing.
  
• Single-target damage is a bit lacking, we sometimes have to switch positions around big enemies and squeeze into them.
  
• All the seasonal weapon enchants are a joke, so the best option is either 'cheat' crit chance with the crit chance based on reserve (and then roll crit chance on all other gear pieces away) or go Puritan and for Supreme crit chance, which I chose to in the end, because I got a good weapon with it.

The difference between my Crusader setup and the TA setup: TA gets the full health tree, puts no point into physical, and just a couple points into constructs.

So without further ado, this is what we do with our Constructs:

Nine skill points. Not one more. It's enough to get them to the hard-cap of damage reduction, because even with a lot more points invested, they will still die on +18 difficulty.
They also won't be dealing any meaningful damage at +18, so they get two defensive modules, and just one with a debuff that the TA can't get himself. Two Destroyers each get one chance to poison, two destroyers each get one chance to hallucinate And of course, we don't want them to misbehave in combat, so they get Phosphor Blasters and Grav-Cannon.

Passives:

• On the crit tree we take everything apart from 'Retaliation'. I mentioned in my TA season start guide that I don't like getting CCed. I know there is a passive in the movement tree that helps, but I have not had the time and motivation to test the build with the morality insta-kill enchant.
  
• Full DoT tree
  
• Heat: All the way to the top, of course we ignore the three that are relevant for actual heat weapons. We just want our heat aura to burn and apply heat vuln
  
• Full Debuff, minus the one knockdown-related node at the right, and an extra 3% suppression damage we can't afford
  
• Full Suppression, minus the 10 hp regen and the movement we can't afford
  
• Full Health, minus the two referring to exposed and overwhelmed
  
• Full Defense, minus the two referring to cover

Perks, Ad-Hoc Subjugation and Cull the Weak are set, the third is a flex spot, I usually have Stride of the Blessed there, on super-hard missions I switch it to Persistent Attrition.

The Crit-Focus is even harder than on the spin2win, here's what I'm sitting at ingame:

Stats:
Full Logic, and all extra points dumped into it. Mindlink and Bionics - for me - are good with 15 from the Milestones, Mindlink gets a couple of extra points if I'm below the damage reduction softcap.

Current items