After soloing Equilibrium, I have some tips for those that haven't done it yet
Have soloed it four times now (getting close to that flawless). Here are some tips I didn't see on youtube:
First encounter:
-Much easier to do this only having to run the gauntlet once than you might think. Recommend praxic blade (at least for the next three weeks) and an eager edge sword to zip around the map. The most annoying part is watching your timer tick down while you're floating towards the next behemoth. Praxic will kill any of them in less than 10 seconds. Use that for damage and eager to get to them quickly.
-First set of three behemoths will drop after you kill the FIRST apprentice. Second set of three behemoths will drop randomly after either the third, fourth, fifth, or sixth apprentice is killed. Final set of three behemoths will always drop after the seventh apprentice is killed, and they are tankier than the first six. Recommend clearing all six normals before dropping in the big boys.
Second encounter:
-Don't get too worried about the generators. I have found that waiting next to one (at least with a sword) while he figures out where you are and does his attack to destroy a generator might actually result in less DPS than if you wail on him nonstop the whole 33 seconds without an extension. Obviously disregard this if you are using a ranged weapon and don't mind blasting him from a distance.
Final encounter:
-If you are trying to three-phase you should definitely kill one shadow, but probably not more than one. Recommend killing the one at the top of the map, since fuck going up there. The high platform in the outer circle where a phalanx spawns is usally a good place to whack that shadow. ALWAYS KILL THE PHALANX and compel a shadow (if one is there) on that platform before you kill the top shadow. Killing guy at the top is usually the last thing I do before going to damage.
-When DPS is over and you have to survive the lightning, try to survive until you are teleported. Easiest way to do this is to ALWAYS HAVE YOUR EYES ON THE APPRENTICE while moving left to right along the front platform where you enter the arena at the beginning. So many of my deaths were because I didn't know where he was. After being teleported to taken realm you have one job: get shadow master. That is all you should worry about. When you are teleported back to the lightning realm, immediately turn around and hit the lock at your 5 o'clock position. THEN PREPARE FOR TICKLE FINGERS. After that wait for the apprentice and kill him. THEN you can go hit the other lock on the left side of the front area. If you try to hit them both before killing an apprentice he will fuck you up while you try to hit the second one.
-When you are being teleported, STOP MOVING. I've had multiple deaths because I was teleported while running or jumping and ran into lightning in the realm I was teleported to or fell off the edge as soon as spawning in.
-During DPS, if you are using a sword, go to hammer town on him until he does tickle fingers. Don't anticipate tickle fingers because he usually does a slam attack right before and if you're not actively fucking him up with a sword while that happens he will physics you right into the lightning around the arena and THEN hit you with the fingers which (1) makes it pretty hard to survive and (2) will crazy fuck up your sword damage rotation. Best time to put away the sword is immediately after he starts tickle fingers since he won't do a slam attack.
-Do DPS prep in the taken realm, which means always finishing the normal realm mechanics first. It's crazy annoying to try and farm super energy, orbs, armor charge, ammo, etc. when getting raped with tickle fingers every 17 seconds. Do that shit in the taken realm where it's safe. After killing/compelling all shadows you can even hang out in the outer ring and take a sip of beer, check your phone, take a breath, etc. Once you're ready and juiced up for DPS, hit the last taken ball and enter hell.
Hopefully this helps someone. Props to Bunghole for giving us a dungeon with an intro encounter that takes five minutes solo and a second encounter that isn't hard (not sarcasm).