This is dependent on good DPS, as you might expect, but it's not a particularly tough achievement. The Maiden of Grief is much like her Karazhan counterpart the Maiden of Virtue in that she has an AoE incapacitate (Shock of Sorrow) that can be (mostly) avoided by taking damage. If you've done Kara, you already know the major "trick" to this fight.
Fortunately, the Maiden herself helpfully provides you with a means of doing this. Periodically she uses an ability called the Storm of Grief, which leaves behind hugely obvious black void zones on the ground that do damage to anyone standing in them. Instead of being knocked out of commission for 6 seconds by Shock of Sorrow, you can watch for the ability (it has a lengthy cast time and should also pop up as a raid warning), then park your toon in a void zone before it hits. The next tick of damage will remove the Shock of Sorrow debuff and put you back in control of your toon.
DoT-based DPS obviously have a slight advantage here, but to be frank, the Maiden has so little health that it shouldn't make a big difference. If you don't want to factor the tank's damage into consideration, each DPS would need slightly more than 2,300 DPS to pull this off; in reality, you'll need a little less than 2K each. This should be well within the capabilities of most DPS classes in decent blues or better, more so once you factor in the effect of trinkets and (if you really need one) a Heroism/Bloodlust.
Brann Spankin' New
As I've mentioned previously, I did most of these achievements as a Druid tank. Before the developers buffed Swipe's threat and then further changed the ability to function independent of a target and 360-degrees, Brann Spankin' New was a relatively unpleasant experience. Half a year later, well...that's still true, but more so due to the carpal tunnel effect that invariably materializes unless one has the foresight to employ a drinking bird on one's Swipe hotkey.
While not the most difficult achievement in the meta, Brann Spankin' New is still fairly demanding. It requires excellent tanking reflexes and experience anticipating the spawn patterns of the mobs, good DPS (biased toward classes with good AoE capabilities), and a healer able to balance the need for healing against the need not to pull aggro against an incoming spawn. If your DPS had problems meeting the requirements for Good Grief or your healer isn't rocking a fairish amount of mp5, you're likely to have issues here -- but most of the responsibility for the outcome lies with your tank.
To that end, your tank should:
a). Wear his/her threat set, and:
b). Position him/herself at the very entrance of the room, on or slightly above the stairs.
The Runed Dwarf adds (and later, golems) will always spawn to the left or right immediately ahead of you. Deploy an AoE threat move when this happens. If you've positioned yourself correctly, you should have a little more than a second to react as they spawn (and the melee adds will typically proximity-aggro and rush the first player they see anyway). Slows like Frost Traps, Earthbind Totems, Crippling Poison, etc. are helpful here, but the beauty of tanking everything around the stairs is that you do have room for mistakes if they occur.
Adds come in two sizes: the smaller Runed Dwarf adds (both the melee and caster versions) and the larger golems. The former don't hit very hard individually and have very little health, to the point where you shouldn't sweat it if a DPS winds up off-tanking a few (and they are increasingly likely to do so toward the end of the fight). As time goes on, you'll see 2 or 3 golem adds. These will always spawn individually and on the right. These need to be prioritized for DPS as they hit significantly harder than their Dwarven colleagues and also have a lot more health.
Toward the end, mob packs will be spawning relatively quickly, and that's when things start to get a little hairy. Most groups lose the achievement at this point by panicking at the increasing number of adds and attempting to DPS them down before the tank has solid threat on them, sending aggro haywire and ratcheting the healing load considerably. It's easy in the middle of this dogpile to lose sight of an add or two on their way to Brann.
Don't worry if you can't kill everything quickly; all that matters is that Brann doesn't get hit. Again, keep the group on or around the stairs, prioritize the golems, keep snares down, CC if you absolutely must, and allow your tank a little more time to build aggro because they'll be spending more of their GCD's picking up new spawns.
If your tank is having difficulty on this achievement, it's worth your time to have him/her practice Brann Spankin' New on normal mode just to get the hang of the spawn patterns and the increasing chaos of the fight. While Paladin and Unholy Death Knight tanks probably have the easiest time with the achievement overall, all tanks are capable of getting through this with a little practice.
Abuse the Ooze
After Brann Spankin' New, this will feel like a fairly sedate achievement for everyone but your healer.
When Sjonnir's health hits 50%, he will begin to spawn small, unimportant oozes that will drift in toward the central platform off the side platforms. Left to their own devices, 2 oozes will combine into an Iron Sludge -- and you need to kill 5 of these. The primary danger from them is their AoE poison ability (Toxic Volley), which adds up to a lot of damage if multiple Sludges are up. Most groups die on this achievement by failing to control their spawn rate.
However, Darsh on the Wowhead thread describes an excellent means of doing just this. When Sjonnir's health hits 50%, have your tank drag him back to the stairs (where the group enters the room). DPS positions themselves on the central platform but should split up; 2 to center area where the Sludges spawn, and 1 to the right (or left, doesn't really matter). The 2 in the center should wait for oozes to become an Iron Sludge and then kill it as quickly as possible (they only have 13K health and will die quickly to concentrated fire). The 1 DPS off by his/her lonesome needs to kill all of the nonelite oozes emerging from that side. This slows down the rate of Iron Sludge creation considerably and, with half-awake DPS, means you should never have more than one Sludge up at a single time.
Your tank will keep Sjonnir occupied (be careful not to DPS him too far down in the meantime), your healer should position him/herself between the tank and DPS, and your DPS should be entirely occupied controlling the spawn rate of the Sludges and then killing them. Get 5, kill Sjonnir, and congratulations; you're all set with Halls of Stone.