The Axkva Min Heroic Encounter is divided into five phases and is perhaps the most difficult of the three initial Heroics to complete.  All of the main bosses are over CL90, and have various abilities and powers that make them even more dangerous than their CL might indicate.

However, with practice, and knowing the technique for each phase, it's possible to complete this instance in under twenty minutes without a single death.

A solid group makeup would include two Jedi, two Medics, and a mix of four DPS and support classes.  Commandos and Bounty Hunters are especially helpful in the remaining four slots, but we have completed it with both Officers and Smugglers in the group, with greater numbers of Jedi or Medics, and overall lesser firepower than a max DPS group.

Two important tips for surviving and defeating this encounter:

1) Make sure each DPS class is equipped with a weapon of each elemental type (even if it's a cross-expertise weapon, such as a Bounty Hunter with an acid pistol). 

2) Under your Options panel, check the box that turns all object names on.

The Chamber of Banishment

After completing the pre-requisite quests to gain entry to the Chamber of Banishment, you'll discover a door in the bottom of the cave at the Nightsister Stronghold, in the location where Axkva Min previously spawned.  Your group can clear the cave on the way down if you like, but it's possible to run straight to the bottom and enter the Chamber.  You are able to click on the door while in combat and be transported to the Chamber.

Once you've entered, the timer will begin on the encounter, and your group will have one hour to complete this instance before the next day's reset.  Even if things go wrong, this is plenty of time.

The Chamber is roughly circular and entered by way of a long bridge.  At the back of the Chamber is a raised altar-like area with five crystals holding the trapped essences of several Nightsister Witches, including Axkva Min. 

It is very important that you do not begin the encounter until everyone has entered the Chamber of Banishment and moved fully off the bridge.  At the beginning of combat in each phase, a Warden spawns on the bridge who will prevent escape.  The Warden will instantly incap and kill anyone who attempts to run down the bridge.  

When everyone is inside the chamber, it is time to begin phase 1.

Phase 1:  Nandina and Gorvo

Nightsister Witch Nandina, and her pet Rancor Gorvo are already spawned in the back of the Chamber when you enter.  The two share a hate list (meaning that generating aggro on one will automatically aggro the other), and also share a buff which allows Nandina to heal Gorvo for a massive amount of health.

Our tactic:  One Jedi aggros Nandina.  As this happens, the first Medic puts stasis on Nandina and Bacta Corruption on Gorvo.  The group nukes Gorvo with maximum DPS while the Medics cycle Bacta Corruption on him.  The Jedi need to maintain aggro on Nandina and attempt to draw her away from Gorvo.

Once Gorvo is dead, Nandina is an easy target to nuke.  When both are dead, return your group to the edge of the bridge and prepare for phase 2.

Phase 2:  Lelli

Lelli can be an extremely tricky Witch to defeat.  During combat, she will repeatedly cloak (causing you to drop out of combat and lose your target).  Jedi Mind Trick may have some effect on how often she cloaks.  It's useful to loop a macro to target her as soon as she comes out of cloak, so you can worry about other things besides tabbing to find her when she becomes attackable again.

In addition to her cloaking tricks, Lelli also drops mines or grenades that debuff your character and trigger the cooldowns on all your specials.  This means you'll be fighting her with autofire only, and will only be able to heal with stims.  Therefore, it's important to keep moving at all times so you're not hit with this debuff.  It's helpful, but not necessary, to have GCW or Officer stims as backups in case your Medics get hit with the debuff.

Lelli herself is not terribly difficult to defeat if you're able to avoid the mines.  The Jedi, however, will have a tricky time tanking her, as standing toe to toe with leaves the Jedi vulnerable to being debuffed, rendering them useless in their role of holding aggro.  A lot of maneuvering is required here.

When Lelli has been defeated, move back to the edge of the bridge and prepare your group for phase 3.

Phase 3:  Kimaru

Kimaru is the first of the Witches with the ability to outright destroy your group.  The phrase "wtfpwned" comes to mind.  In addition to being a CL92 gold boss with over 600k health, Kimaru has some nasty abilities that will tear your group to pieces.

The first of these abilities is a fire ring that she will spam all over the Chamber.  Towards the end of the fight, the Chamber will literally be wall to wall with them, with only very narrow passages in between.  Running through, or standing in a ring of fire deals massive damage.

The second ability is Force Storm, a lightning-like ball of Force energy that Kimaru uses in conjunction with the rings of fire.  These also deal massive amounts of damage if they hit you, although running through them seems not to deal any damage.  To be safe, however, the Force Storms are easier to spot if you have "all object names" turned on, as you'll be able to see them better.

To defeat Kimaru, your main Jedi aggros her, and the remainder of the group starts moving around the chamber, never stopping motion.  Just as with Lelli, even your Jedi tank needs to keep moving, or he'll find himself standing in a ring of fire and a Force Storm and dead within seconds.  Movement speed is really helpful here, so Force Run, Power Assisted Sprint, Sprint Stims, Accaragm, or, best of all, Officer Charge and Scatter specials, are very helpful here.

Keep moving and keep shooting, avoiding the rings of fire and the Force Storms, until Kimaru is defeated.  Regroup at the base of the bridge (mind those rings of fire until they despawn) and prepare for phase 4.

Phase 4:  Suin

This is the make or break phase of the Axkva Min encounter, and the single most difficult straight-up fight you'll encounter in the game.  Like Kimaru, Suin is a CL92 gold boss with approximately 600k health.  If your tactics and group play are weak here (especially communication), your group will be destroyed in seconds flat.

Your main tank will aggro Suin, and can attempt to tank her toe to toe as long as he/she is able.  Two Jedi can trade off tanking, though she can be difficult to taunt if you have Bounty Hunters and Commandos doing massive DPS.  Suin also seems to have a thing for Medics, and I've seen Medics end up tanking her, despite the Jedi's best efforts at taunting.  If this ends up being the case, movement speed is essential.

Suin herself is a tough fight, but she brings friends.  Moments after the encounter begins, Suin will summon minions to help her fight.  These are CL90 gold bosses, but with a twist:  each one can only be damaged by a weapon of a certain elemental type.  As soon as the minion is attacked, a buff icon will appear under her name indicating the type of elemental damage she is vulnerable to.

We have one Jedi tank Suin while the group goes to work on her.  The off-tank Jedi watches for the minions to spawn, and attack them as they appear.  The Jedi then calls out the vulnerable elemental type, and one of the Bounty Hunters or Commandos can switch to the appropriate weapon and help the off-tank kill the minion.  The core of the group remains focused on Suin.

This is a hectic and dangerous phase.  It's easy to become overwhelmed and end up with as many as seven CL90 minions helping Suin at one time.  It's vitally important that your off-tank identifies each minion as she spawns and calls out the elemental, and helps a pre-designated Bounty Hunter or Commando kill her.

During the times when there are no minions, the entire group can be focused on Suin, and finally, with good tactics and lots of firepower, take her down.

You're now ready to regroup for the final phase.

Phase 5:  Axkva Min

When Suin has been defeated, the Essense of Axkva Min will come to life and slay the Eternal Warden who guards the bridge out of the Chamber of Banishment.  Despite your bravest efforts, Axkva is about to escape!  It's up to you to stop her!

Axkva Min is a CL92 boss with 1.1 million health.  Similarly to Kimaru, Axkva will spawn numerous Force Whirls that deal incredible damage, while she herself is a melee nightmare. 

The tactics are the same as those for Kimaru.  Identify the Force Whirls by having "all object names" on, and avoid them at all costs, while also dodging Axkva, who's aggro is difficult to control.  One thing we have noticed is that it's fairly easy for the medics to keep a low profile during this phase, and they can effectively focus on healing.  The edge of the bridge and the altar area at the rear of the Chamber seem to be fairly safe places for a Medic to hide out and keep tabs on the group.

While avoiding the Force Whirls, hit Axkva with everything you have.  She's fast and she hits hard, so it's important for your Jedi to communicate and attempt to trade aggro (and for your Bounty Hunters to have Shields ready just in case).

Pour as much DPS into Axkva as you can, and avoid the Force Whirls, and then rejoice as the Nightsister Queen is defeated! 

For defeating Axkva Min, you receive a permanent bonus to Critical Hit defense, and a token of your accomplishment to trade in at the Township of Aurilia for nice statted jewelry.  In addition, the villagers of Aurilia will randomly compliment you on your brave victory as they walk past! 

Axkva Min drops one of two schematics as loot:  the Juyo Lightsaber Schematic (no trade), and the Nightsister Carnage Beret (tradable, requires Domestics IV).

Tips

As stated earlier in the guide, make sure to bring a wide variety of elemental weapons, and be prepared to communicate well.  Group coordination is vitally important to winning this encounter, as you're not going to live long just trying to DPS it to death.

The encounter is on a one-hour timer for the day.  If your group perishes during the fight, it is possible to clone to the nearest starport or bind location and run back.  Until the hour is up, you'll be able to re-enter the Chamber of Banishment and pick back up where you left off (unlike the IG-88 encounter, which resets to the beginning if you are defeated).

Good luck!