How to make fearless deadly stoic volatile prisoners do their time?

The solution⁵ to a proper supermax involves barred walls and armed guard patrols. In a regular setup, the following staff can get into contact with legendary prisoners:

• Guards: When attempting to quell their random raging rampages.
• Cooks: When delivering meals to their canteen.
• Janitors: When cleaning their cells.
• Workmen: When repairing the stuff these prisoners destroy¹.

An example design for a single cell is below to illustrate the point.

x    Secure door
d    Remote door 
=    Wall 
+    Barred wall
c    Canteen
l    Cell
a    (Armed) guard patrol
f FAST flooring

Gang leader // unpunished version

ffff
f+=d=+=
f+ccc+a
f+ccc+a
f+ccc+a
f+ccc+a
f+ccc+a
f+=d=+a
f+lll+a
f+lll+a
f+lll+a
f+=d=+d

Permanent lockdown version 

+=x=+=
+lll+a
+lll+a
+lll+a
+lll+a
+===+d

Our crazy fruitcake prisoner has to be in vision of a guard. Usually, these prisoners are 'tough/extremely tough' making them resist tasers, in which case a freefire armed guard is necessary. Otherwise, a pair of regular guards get the job done.

If we're not dealing with a gang leader, it's possible to use permanent punishments to put the prisoner on permanent lockdown. Thus, the large construction for the gang leader is only needed 3 times³.

The cell and canteen⁴ should contain all the necessary items to take care of (most of) the prisoner's needs.

When a legendary prisoner invariably acts up, instead of a guard response team needing to get to them, they're always already in vision of an armed guard, and promptly shot. A single shot typically does not kill these prisoners. Non-tough specimens can be tazed instead.

Alternatively, a yard can be placed in between the two rooms, and a sniper tower can handle multiple of these 'single-prisoner-prison-within-a-prison' constructions.

The remote door in the center can be attached to a door timer, freeing up some guard time. Pressure plates can be installed in front of the remote doors to get deeper into the mini-complex for some more savings (though obviously not for the way out).

A proper regime is necessary to make these things work. For the gang leader version: Typically the regime would consist of 8 hours of sleep, 1 hour of shower or lockdown, 3 hours of eat, 5 hours of lockdown, another 3 hours of eat, and 4 more hours of lockdown.

Then, during the 'eat' time, you can instruct janitors to clean the cells using the new 'janitor deployment' feature from the Bucket update. By assigning a janitor to each cell during the 2nd and 3rd hour of eating time, the cells are cleaned while the prisoner is in the canteen, and the janitor won't step into the cell while the prisoner is in there, at least in theory². If you use the permanent punishment version; janitors can clean during 'sleep' time as well.

As a failsafe against escape attempts, the access roads to the complex should be covered by sniper towers. A couple towers can cover many complexes if built correctly.

As a failsafe against (armed) guard foolishness or bravery, whatever you want to call it, it's important to make sure there's no fast route from the behind-barred-wall guard patrol to the prisoner.

If you want to give the prisoner visitation rights, it is possible to attach a visitation booth to the bottom of the cell in its own little 2x4 visitation room.

Another alternative to attach is a 3x3 cleaning cupboard to the bottom (with no exit), for a combination of cupboard, cell, and canteen. By using work/lockup and adding a single prisoner employee to the cupboard, perhaps the prisoner can clean their own cell, as the janitor is really the hardest employee to work around not having. Of course, this version won't work for gang members/leaders, who refuse to work. It also leads to unavoidable overdose, for bleach is a prisoner's favourite drink. Trying to prevent thievery via adding a dog handler to sniff the inmate of doom periodically is animal abuse, or, if you're lucky and the prisoner butchers the handler, a bit of canine revenge carnage.

1. Workmen are at less of a risk as the prisoner tends to be cuffed while they work, as long as you don't queue up too much stuff for them to build at once, or prioritize/micromanage the supermax wing. If it takes too long for a workman to arrive, the taser or unconsciousness may have ended and they are vulnerable.
2. However, pathing is kind of stupid, and doesn't consider closed remote doors as obstacles, so it's important that any path into the cell, even from the front door of the canteen, never goes through the canteen. This can be engineered by adding a little path to the left of the cell made from a fast material such as racing track or concrete, and filling the cell and canteen with slow material such as padded flooring. You may find janitors still 'sometimes' doing the dumb thing, but not always.
3. However, any single-room construction will mean janitors can only clean during 'sleep' time.
4. The 'room of choice' for a two-room setup is the canteen, since it's necessary for any multi-room setup: only punished prisoners are fed in their cells.
5. Financially, this solution isn't very workable long-term if all your prisoners are like this. Fortunately, legendary prisoners pay enough at takein that this is doable.