For Mirrored Soul I have my team set up where all DPS targets a fellow team member to stop attacking. My healer switches from direct mouseover healing to focustargettarget so heals automatically land on whomever DoS has targetted. This allows me a bit of flexibility to reposition. When the red beam stops, DPS can start again.

Everything else beyond that is movement. Not just left and right, but backwards and forwards, too. I also make use of multiple follows and limited follow distance/interact to take advantage of positioning.

If my tank gets the Wailing Souls debuff, I can immediately make my other melee DPS follow one of the ranged toons to get them out of the way. If one of my melee DPS gets the debuff, I can run forward through DoS, separating the cluster, then interact to get everyone to the boss and a quick follow to get them behind the breath. Running forward being the key there, as it gets my ranged toons closer to my tank so there is the least amount of distance possible for them to cover for interact and follow, so they are easier to round up for safe positioning and a quick chain heal. This is the point where I start blowing cooldowns since I should have at least 10 seconds where I'm not line dancing, mirrored or goo dodging.

I also make use of interact and opposite strafing to get my toons out of puddles of Owie. Since I always try to have my tank facing my melee DPS, whichever direction I move my tank using alt movement keys, my DPS moves away, but the mob moves with my tank. So if DoS is dropping puddles on my melee toons, I can move backwards or strafe out of the puddle, the mob will move forward to follow my tank, leaving a clear spot for my melee DPS to go back to. Since the melee toons have almost certainly turned slightly during combat, they move diagonally from the tank, avoiding most if not all of the puddle, and come back in straight. For my ranged, I can abuse interact to keep them from going out of range while I strafe them around.

The biggest assets during this fight are the ability to move and keeping calm {and zoomed out!} enough to watch what's going on. Panic is the killer here. Hold your cooldowns until you can get the most use out of them so they aren't wasted on high mobility or no DPS phases. If things go bad, you can always use the hallway to reset and regroup.