I've done the DM East boss run a couple of times now so I will do my best to recall the needed steps for you. An entire run, if done properly, takes no more than 45 minutes.
Please note that this will not be 100% accurate until a couple of edits! I will need to verify some steps during my next run and update this guide. It should get you started though.
As soon as you enter the instance, head for the Imp (6). Move past him out on the corner of the ledge and jump right out from the "pointy end" of corner.
Jump too far to the left and you will aggro an elite flower-thingamajig, jump too far to the right and you will aggro a whole bunch of non-elite flower-thingamajigs.
After you land, move up towards the norhern wall and in towards the huge tree (part of the level, not an NPC) -- not too far or you'll aggro another NPC-tree behind you. Heal up before you move along.
Keep an eye out for packs of roaming tree-things. They travel in packs of three and are quite fast. There is one that patrols near by the spot you landed when you jumped down.
Once that pack has moved back up along the road, hug the northern wall and head east. At the north-east corner there is one elite flower. Kill it.
Hug the eastern wall and start heading south, once again keeping an eye open for packs of patrolling trees.
Approximately halfway along the eastern wall you will happen upon another elite flower. Have the tank pull it a bit further south from where it is standing so that you don't aggro the patrolling trees behind you. Kill it.
Continue south along the east wall. Keep an eye out for any patrols and when in the clear enter the hallway at the far end of the eastern wall. Look out for invisible satyrs in these hallways.
Hug the right wall until you reach the pool of Hydraspawn. This bugger knocks you about and disarms you but should be an easy match for any reasonably equipped group as long as you're not knocked into another mob. He spawns two lesser mobs when he gets low on health. Nevermind trying to cleanse his debuffs, he hits the entire party with loads of them so you'll have to wait them out instead.
Continue north-east across the pool, aiming for the stack of skulls in the corner of the pool. Climb over these and then head across the room, going slightly diagonally (sort of east-north-east). Make sure you don't aggro the elite flower just north of you.
Hug the right wall until you reach the hallway leading up to the upper floor where Zevrim Thornhoof lives.
As soon as you reach the top, turn left and hug the left wall. Follow it as far as you can with Zevrim to your right.
Zevrim has a special attack where he puts one of the party members on his altar and starts torturing him/her. If this happens to the healer you need to be ready with your healing potions! Also make sure that you head the right way when his attack releases as you could easily run into the mobs on the other side of the altar.
The tank should also try and keep Zevrim as far away from non-melee classes as possible as he has an AoE shadow damage attack.
After killing Zevrim you go to the south, towards the ledge, keeping to the right. You will see a pillar just next to the ledge and just below it an elite satyr with 4-5 non-elite imps.
Jump up on the pillar and then let the tank jump down and aggro the mobs. Kill them ASAP without aggroing the other mobs across the room.
Hug the right wall and keep on heading south, towards the hallway leading upwards to Lethendris and Pimgib.
As soon as you reach the top you'll notice another ramp right in front of you, follow this one and you'll reach the section where Lethendris is.
Take out Pimgib ASAP as he grows bigger the longer you fight him. After the fight is over make sure to check in the back of the area for a dusty old tome that might have spawned. This can be any sort of DM book.
Head back down to where you fought the satyr and the imps by the pillar and turn left (you are now at the hydraspawn pool). Keep turning left and head out towards the main courtyard in the same fashion you came in (hugging the proper walls etc.)
Once you reach the courtyard, in the north-east corner of the map, you will have to do one of two things depending on how your party is set up.
1) If you have a rogue, send him up the road to talk to Old Ironbark. Just make sure he doesn't aggro any patrols. Note that it can be tricky to get Old Ironbark to talk, you will almost have to stand inside one of his legs for it to work. The rest of the party backtrack the same way they came in, hugging first the east wall and then the north, until they reach the door in the northern wall.
2) If you do not have a rogue you will have to clear out all the patrolling groups of trees. They are not especially tough, just make sure you do not aggro anything else. After this, any member of your party can talk to Old Ironbark. Head up to the door in the northern wall.
Note that you will have to kill Zevrim in order to be able to talk to Old Ironbark to begin with!
Old Ironbark will destroy the door that leads to the section with Alzzin the Wildshaper. Again look out for invisible satyrs in the hallway.
Once you reach the big hall of Alzzin you need to be on the lookout for a huge patrolling tree. You can either wait in the doorway for it to appear and kill it or hurry across the road and up on the ledge before it spots you.
You need to get up on the ledge in order to avoid aggro from all the mobs but getting up on this ledge is probably the trickiest part of the entire run.
Straight ahead from the doorway that you enter through and a little bit to the left is a pillar (or a tree) with a couple of small rocks behind it. With some careful timing it is possible to jump up on the ledge from these rocks.
Follow the ledge to the left down to the bottom of the hall.
As you get down to the bottom, make sure that everyone walks down the small slope so that you do not aggro the patrolling tree (unless you killed it before).
Take out the groups of elite + non-elite flowers, preferably starting with the left one and then the two right ones to give you a bit more space to manouvre if needed.
After this you take on Alzzin. He changes shapes from a satyr to a tree to a wolf and then back again. One form is a caster, one is a tank and one is a damage dealer.
After he reaches a ceartain health adds will spawn from the furthest wall. These imps don't hit very hard and don't have a lot of health but there are plenty enough to kill your healer if you're not careful.
Here is the only situation where you really need a mage or a warlock with powerful AoE. A warrior might be able to tank them all if good enough though and it is doable without a caster albeit tougher.
After Alzzin is dead you can head up through the same hole in the wall that the imps came through. There are three rich veins of thorium to be found in the tunnel.
After exiting the instance you leave the tunnels through a trap door and then a hallway to your right.
If you wish to repeat the run, the entrance to the instance is to your left once you reach the main Dire Maul courtyard.
