..Continued from above comment...

As you hit the lava (AH!) turn left and jump-swim to the wall on your left. Jumping seems to help you take less damage but maybe be ready to take a health pot before you clear the lava. If you run along the slope away from your pet real fast you may be able to get far enough away for him to disappear before he dies, saving you from one rez/feeding later. Stay to the left, running and jumping until you cant go any farther on the slope.

You'll run out of slope with a wide pool of lava to your right. There is an island out there with 4 fireguard on it. In between you and the island is a Fireguard pathing around unseen below the surface of the lava. Have elemental tracking activated and click around in the lava till you select him. Hunter's Mark him so you can watch his movements (he goes too far under the surface sometimes but you see the mark every few sec). If you're in a group and leader (doesn't matter where in Azeroth the other player is) you can use Raid targets also, these may be easier to see). When he's a pathing away from you to your right jump in the lava and head for the island. I took a health pot here but might have made it without. You want to just barely get on the tip of the island and stop so as not to agro the 4 Fireguard there.

Heal up and summon your pet. Turn to make sure your pet doesn't summon right in the lava or it'll die real fast (duh! sorry kitty). Send the pet in to attack the Fireguard on the back left and run in a few sec later. Run past and jump off the back left side of the island, jump/swim through the lava to the 1st landing you can get to. I had a Fireguard coming after me and feigned once I hit the landing. Let your pet die and then rez them. Up the ramp and to your left is your goal. Two groups of 3 Fireguard guard the ends of the bridge leading to the Molton Core portal. Your core fragment is to the left of the portal. Send your pet to the 1st group and run past. When it dies and they come after you feign in the middle of the bridge and let them reset. Same for the next group, but when you feign do it behind the core fragment. When the group resets pop up and grab your fragment! Do a little dance! You did it! Now if you're in a group or have a friend somewhere that will join with you, convert to Raid (open your Social window, click Raid tab at bottom, and click on "Convert to Raid"). Jump in MC portal, jump back out and it'll take you right to Lothos to turn in the quest. Ta-da! you're done.

I did a video of the whole thing but I used fraps and it split the move into 2 files and also I play at 1200x1600 and even at "half size" capture the files are huge. I may try it again using real small screen resolution. Until then I have a bunch of screen caps.

Edit: Screen caps have been removed after so long so here are some links:
http://i3.photobucket.com/albums/y87/JohnPowers01/SoloHunterAttunement4x400.jpg
http://i3.photobucket.com/albums/y87/JohnPowers01/SoloHunterAttunement4x401.jpg
http://i3.photobucket.com/albums/y87/JohnPowers01/SoloHunterAttunement4x402.jpg
http://i3.photobucket.com/albums/y87/JohnPowers01/SoloHunterAttunement4x403.jpg
http://i3.photobucket.com/albums/y87/JohnPowers01/SoloHunterAttunement4x404.jpg
http://i3.photobucket.com/albums/y87/JohnPowers01/SoloHunterAttunement4x405.jpg
http://i3.photobucket.com/albums/y87/JohnPowers01/SoloHunterAttunement4x406.jpg

I was looking at how to solo attune for MC on a few sites online. It's apparently easy for rogues or druids with stealth but I thought I'd try using a hunter's skills. I bought several Invisibility and swim speed pots but didn't need them. I'm a level 60 NE Hunter on Durotan with 2529 armor and 3397 health, nothing special. I had the Shadowforge key so I was able to open the 3 doors you need to get through by myself. If you don't have the key you'll need someone to open them for you.

The first door is immediately to your left as you enter the instance. Go through that one and enter the room hugging the right wall and avoiding the patrol and open and go through the first door on right. Go to the first door on your left and open it being careful not to run right in because there may be a patrol coming down the stairs directly in front of the doorway. Once the Fireguard patrol goes by run up the stairs keeping to the left at the top of them.

The room at the top of the first flight of stairs has several groups of mobs off to the left of the stairs and 2 Fireguard patrols. You want to avoid the ones on either side and once the patrol has gone around the corner, wait about 5 seconds and run straight for the 2 dwarves at the start of the hallway (you'll be facing Northeast at the top of the stairs). You're going to try to agro just those two, go around the corner, hugging the left wall so as not to agro the group in the corner off to the right. Once you're about 1/3 of the way down the short hall, Feign Death and the two dwarves should reset. You should time your Feign to be able to come out of it and not catch agro from any one of the groups around you, also watch out for the Fireguard pat. There is a group straight ahead on the right so run forward hugging the left wall. You'll see a window as you round the corner with one dwarf standing there. Run straight through him and jump out the window. As soon as you do you'll lose agro. Be careful not to run right off the ledge below the window. You want to go left as soon as you hit the ledge and jump down to the bridge below, staying away from the group in the middle.

A few other options: On my first attempt I did the room differently. I have the Stop Watch trinket (+40% speed for 10 sec), that allowed me to run right through the room, down the hallway and out the window and I had about 1/3 health left. You don't get dazed when hit using the trinket. There is a 30 min cooldown though so on my next try I decided to save the trinket and do it the way I describe above. You can also use your pet. Sic him on the 2 dwarves and run past, calling him back to you as soon as you pass. You should both make it out the window alive.

When on the bridge stay to the right to avoid the group and then move to the center and go right between the elementals. Keep to the middle and head straight down the hall toward Incendius. You shouldn't agro the first two pairs but the last pair before Incendius is too close together. I died twice just running past them because they do a fair amount of damage and once I hit the lava I was gone before I got through. Use your pet. Time it so that as you run through to jump off the bridge Incendius will be on the far side of his path and won't notice you. Send your pet in to agro this last pair and run through to the bridge, immediately jumping off to the left.

Continued in the next comment....

This attunement can also be done for many people with just one run (useful for a guild attunement). Players above the 5-man limit who want attuned are to gather just outside of the instance when group is nearing core fragment.

1) Be sure to have a Warlock in the party.
2) Proceed as Dread suggests and grab the core fragment
3) Make the warlock party leader and remove 2 members from the party. Allow them to hearth back to home city.
4) Invite 2 more people who should be ready to enter instance
5) The 3 players remaining in BRD summon the 2 new players to the core fragment area once they have entered instance. New players grab core fragment.

Rinse and repeat as necessary until all your friends are attuned.

The Core Fragment can be found to the left of the Molten Core portal, inside Blackrock Depths.

The portal to MC is near teh black forge if that helps, if not...
Begin by going through the gate to the left of the entrance to BRD, then go through the gate to the right, then the small door (all of this requires shadowforge key). then go up the stairs and take the path to the left. You should come upon 2 windows, one leading onto a bridge, and teh other to a road, jump out onto the ledge to the bridge and tehn onto the bridge. Theere may or may not be a group of mobs waiting for you. if there are, kill them, and then proceed towards incendius ( fire elemental boss next to the anvil). After he is dead jump down to the left and continue in this direction untill you get to a wall/ledge jutting rather higher out of the lava. Use TAB to find the elemental hiding in the lava have a hunter or mage pull him (warrior and rogue bow range might not be enough to reach it)then heal up and lava jump across to the small island, note that there are 4 elementals standing on it, if you are very careful not to get any closer than you absolutly need to be to stop taking fire damage, you should pull unless you are below lvl 57. after they are dead (pulling 1-2 at a time) jump across to the ramp and then stop where it splits off into 2 paths, one leading to the black forge and one to 3 linked elementals. If you have a warlock, banish is recomended. Kill them the go along the bridge to the MC portal, kill the group of mobs, and look to the left of the portal. There should be a stalagmite/tite,cant remember which is which ><, on the ground, inside is the core fragment. Convert to a raid and eneter MC and then leave to quickly get back to lothos to complete the quest. Warning: If you enter MC without getting the fragment you will have to go all teh way back through BRD again to get it as you will be next to lothos and not even in the instance anymore.

Quick walkthrough on how to solo with stealth?

http://www.ultimategamers.com/worldofwarcraft/blackrockdepths.html

there's a map, and I know the instance perfectly up to plugger/black anvil

but, where in BRD is it?

One handy tip to note - you can complete the quest in spirit form (i.e. Dead!) as I discovered during a rather unfortunate wipe...