Any class can do this!
Requirement - a significant speed cd or consumable and a blink, leap or immunity (any class can do this with soulshape and engineering as shown).
Strategy: Stand at the left/south side edge and kill the mini boss there - as soon as it dies, sprint up to the pillar if the boss activates it (50% rng so you can get unlucky and need to reset) with all cds you got at your disposal. You need to avoid the blue beams and the bots on your way up because they teleport you back, and you can do it by teleporting, leaping or using an immunity.
When you solo this, you have exactly 3 seconds of possible downtime and its basically spent on avoiding the 2 bots at the top so you have little room for error (you can immune those i think and keep casting).
You have to get to the top before the boss starts casting in the middle - this means you have to beat the boss' travel time to the middle.
This is much easier when using class utility from basically any class that isn't a dk or priest (they gotta resort to using speed increase + soulshape like i showed) - fx mages can blink almost the entire way, monks and warlocks can pre-place a teleport that avoids all the difficult stuff, demon hunters and warriors can leap a big distance and hunters and paladins can just run through with an immunity (i didn't use my immunity for the sake of showing its doable without class spell usage).
You can also make this easier for yourself by equipping speed gear and fx using Ripple in Space major essence for a teleport, however its still doable with no investment.
