This hardest part of this boss lies in phase 1, which in a nutshell, is just another big fat DPS check. Conventionally the fight starts with splitting the raid in 2 groups where each group goes to their assigned platform and DPS the add down, and both adds needs to die within 10 seconds of each other or else they come back to life. Each add is linked to a tesla coil and if kited too far away from the coil, the link will break, dealing 6k raid wide AOE damage.
When soloing this encounter, the player can only be on one platform at one time, therefore it is inevitable for the add on the other platform to come over and thus loses its link with the coil, hence dealing 6k AOE damage. Therefore the incoming damage during the first phase is not only from both adds, but also from the tesla as well. This means that both adds must go down at the same time before the damage becomes too overwhelming. It does not really matter as to which platform to choose when starting the encounter, however there is a slight advantage when starting with Feugen as the Magnetic Pulls will always be used by Feugen. Since the player is already at Feugen when this happens, Magnetic Pull won't have much effect. If the player decides to start with Stalagg, Feugen will cast the first Magnetic Pull before he reaches the player, thus pulling the player away from his platform and this may cause Stalagg to also break his link from the tesla.
From a priest's perspective, 4pc T13 is definitely needed for this fight and it should be used when the second add arrives. Let the dots finish the first add, while using the 4pc bonus to burst down the second add. If RNG is good, they should go down together. If RNG is not so great, keep in mind there is a 10 second window to finish the other add off should the first one die early. However by this point it also highly likely that a wipe can occur due to taking excessive damage.
Once both adds go down, phase 2 starts and that is the actual fight against Thaddius. The fight itself is purely tank and spank, but just to remember to get into his melee range as soon as possible. Also don't forget to jump/levitate when moving onto his platform.