One of the easier heroics overall, the Nexus is also home to three achievements. None of them are as difficult as the achievements found a few stories up in the Oculus, but they still require some coordination.
Not a really tough achievement, but a single group member can wreck this if they're not paying attention. Grand Magus Telestra splits herself into three forms (Frost, Fire, and Arcane) twice over the course of the fight. In my groups, players usually elect to kill the Frost version first because her Blizzard ability is a problem for melee DPS, but to do Split Personality you need to make sure that all three copies die within 15 seconds of each other on both occasions that they're summoned. This is most easily accomplished by having all party members use Shift+V (or whatever option you're using on your computer to force mob health bars to materialize above them) to monitor the clones' health at all times.
Once you have mob health bars up (or if you have someone who's just tab-targeting through them and calling out their health percentages over vent), from that point, it's a relatively simple matter to kill the clones within 15 seconds of each other. The one snag you may hit is that the Frost copy cannot be killed if she's channeling Blizzard, but Blizzard can be interrupted. Assign an interrupter to keep an eye on her. If you don't have classes with low-cooldown interrupts in the party, you'll have to save one for Blizzard or, for safety's sake, refrain from killing the Fire and Arcane copies until after the Frost copy finishes channeling.
If you have any amount of AoE in the party, this achievement should be the easiest one in the Nexus, and I've seen more than a few groups get it without realizing it even existed.
Explaining this achievement can be somewhat time-consuming, but while reading through various comments around the net to make sure my own take on it hadn't missed anything, I realized that the best thing I can do is to point you in the direction of comments written on the Wowhead thread. Phazz's comment in particular gives a very good explanation of what the achievement entails, and does so without needlessly complicating things. Frankly, he/she did a great job, so I'm going to point you in that direction rather than pretend I could improve on that take.
I will add, as someone who's tanked this achievement quite a bit, that with good DPS you're unlikely to have to move too far before Anomalous finally dies, and you can abuse the narrow ramps on the platforms leading to him in order to funnel all of the non-elite adds emerging from the rifts. For undergeared tanks with limited AoE threat generation, this is the best of your options, as the adds will be forced to aggro directly through you and can be picked up if you so much as sneeze at them. Assuming that your group maintains 15+ yards range on you at all times, not only will you be absorbing all of the rift damage, but there's essentially no chance that any adds will reach your group.
This is a very, very easy achievement for some classes, but not much fun for others. Happily, though, it's an individually-based achievement; if someone in your group screws up their own Intense Cold stacks, you can still get the achievement for yourself.
As most players will already know by now, Keristrasza casts a debuff called Intense Cold on players, and will recast it every 2 seconds for the duration of the encounter. The only way to prevent it the debuff from stacking is to keep moving. That's easy enough (albeit tremendously annoying for caster DPS and Hunters), but what eighty-sixes this achievement for most people is her Crystal Chains ability, in which she will freeze the entire group in place for 10 seconds. If you don't have a way to get out of Chains (or have someone else get you out), the achievement isn't doable, because even with monster DPS Keristrasza is certain to get at least one Chains cast off. Thus, assuming that you move enough to keep Intense Cold from stacking more than twice, the achievement is mostly about getting yourself out of Chains quickly.
I started making a list of class-specific skills you can use, but must admit that for some classes I'm at a loss, so comments on this are most welcome:
Death Knights: Truthfully, I'm not sure. The only thing I've seen mentioned anywhere is the Unholy talent Anti-Magic Shield, but I don't actually know if it removes or prevents Chains. As an aside, please, oh please, do not use Army of the Dead on this fight. Watching Keristrasza freak out and turn every which way to attack the legion of ghouls is hilarious, but less hilarious is your melee DPS and tank getting tail-swiped all over the room.
Druids: Shapeshifting will free you from Chains. If you're tanking, make sure you have a shapeshift macro that will allow you to shift to Dire Bear from Dire Bear (/cast !Dire Bear Form should work). No Druid has any excuse for missing this achievement.
Hunters: If you're Beast Mastery, The Beast Within will render you immune to Chains for the duration of the ability, or get you out of Chains once they're up. Master's Call will also work. If you're Marksmanship or Survival, I'm not sure.
Mages: You can both Ice Block and Blink out of Chains. As Keristrasza is unlikely to recast Chains while Blink is on cooldown, it probably doesn't matter which you decide to use, but to be on the safe side (especially if you're running with a group with mediocre DPS), you'll probably want to use a Blink -- Ice Block -- Blink rotation. If Keristrasza manages to get more than three Chains off, your group should probably not be doing heroic achievements.
Paladins: Divine Shield and Hand of Freedom will both work, as will Cleanse. If there's no Priest in the group, you can reasonably expect to be Cleansing other players who don't yet have this achievement and may not have any options for getting out of Chains.
Priests: Mass Dispel is your buddy here, and it'll also be the buddy of any class that can't get out of Chains on their own. If you're the designated butt-saver for this achievement, force the group to clump up as much as they can without subjecting themselves to tail-swipes or the frontal-cone AoE so that Mass Dispel will hit everyone.
Rogues: Cloak of Shadows and Vanish are the most obvious choices here, but 2/2 Improved Sprint will also work.
Shamans: This is another one I don't know about. Thoughts?
Warlocks: Yep, need some help here too; the only thing I could find was the post-3.0.8 Demonic Circle.
Warriors: Intervene will work for Protection Warriors: I'm told that Heroic Fury should work for Fury Warriors: otherwise, I'm not sure.
If all else fails and you're a class or spec without a Get Out of Chains Free card and you don't have a Paladin or Priest in the group, both a PvP trinket and a Free Action potion will work (although, depending on your server, the latter may be tough to find on the AH as it uses only low-level materials that also require a fishing trip). With competent DPS, Keristrasza should die before she casts a third Chains (and certainly before she casts a fourth).