Kill the guys in the main room-- opens a red and yellow portal.
(NOTE: Make sure your party is with you when you start each event. You cannot go through portals once events have begun)
Through the red portal, you just keep killing things as they come.
Kill the Portalis Recallers when they are up. That will prevent the adds from coming in. They spawn near the center and move towards the boss where they become killable.
Fight the adds in the center of the room to prevent extra damage from standing too close to the boss.
The Chargeresses and Warlords (epic), hit a fair amount harder, so really it's just an issue of aggro management. Once the event is done, collect the purple shard from the orb at the purple portal.
Through the yellow portal, you need to be a bit more aware of what you're targeting. Kill electro-sell warbots until the energized battletech arrives. You don't want to kill the unstable conduc-tok. Any warbots that are alive when the battletech dies will become an overcharged warbot and they hit substantially harder than the reg warbots (It's probably a good idea to burn them down if healing/damage becomes an issue). Don't stand in the green stuff when you kill the battletech. Also, don't stand super close to Insider Pinboggle-- he wrecks your stats. After two rounds, click the orb by the green portal for your green shard.
Back in the Main Room: Zom Xakra'Kaas and Zona Centi'Kaas is a linked encounter. Basically, Zona is the pain of the pair. You use the purple shard to root him in place. He forces your target to him if you're too close, so once you're 10-15m away, you should be able to attack Zom. The purple-shard root only lasts for 10s. You can be pro and proactively keep Zona rooted in the same place, or just wait until he is free and on you again, root and move Zom again. You get a better burn on Zom if you keep Zona locked in place, but... that's just an efficiency thing-- not necessary. Since you're given a limited supply of shards (one per person), it's probably not a terrible idea to come up with an order in which you want folks to use their shards. If you don't kill Zom before you run out of roots, have no fear, you can just AE him down the rest of the way. There's green text for the green shard... use it.
Zona has red text that calls out an individual-- that person will get an uncureable trauma that hits them (and others near them) rather hard... they should move away.