Walkthrough (pre- Cataclysm) Edit
The temple is split up into two main sections, separated by staircases (or the deadly hole in the middle of the upper pit), the first is mandatory for completing the main run of the dungeon (where you defeat the Shade of Eranikus), whereas the second section is the basement - a completely optional section, however there are two enemies there that have good drops (Spawn of Hakkar and Atal'alarion). Each of these two main sections contains a few floors - the main section has a top floor, a middle section (balconies), and a bottom (the dragon pit area). The basement also has a top and a bottom.
If you don't have a lot of time to spare, stick with the main section and focus on the related quests or loot you are looking for (for experience, just explore wherever). However, if you do have time to take on the basement, you'll want to go there first.
Optional: The Basement Edit
From the start of the instance, head forward and to the left. Run down to the bottom of one of the stairwells (not the two spiral staircases available from the entrance of the instance). The hallway area you reach is a giant ring around the main floor of the basement; this hallway contains Murk Worms (aggressive) and maggots (neutral), however, the maggots will aggro if you get in a fight so if there are any you can pick off, it's better to be safe than sorry. Note that there is sometimes a rare spawn that patrols this hallway, Spawn of Hakkar (it looks like a wind serpent).
Inside the circular hallway there are tunnels that lead to balconies in the inner chamber. Each balcony contains a serpent statue - by activating the statues in a specific pattern (south, north, south west, south east, north west, north east) you will summon Atal'alarion. If you want to save time here, you'll have to try and minimize the number of groups you take on in the circular hallway (although the running distance to avoid mobs may be just as burdensome).
After summoning Atal'alarion, jump down to the left of the balcony you are standing on and clear the mob and any patrols around you. Heal up, and hop down into the shallow water. Wait for Atal'alarion to move away from the Murk Worms and try to pull them without aggroing him - fighting them together can be painful. He hits hard, so try to stun or CC him and keep your tank over healed (if you have someone with additional healing abilities you may want to use them; potions are also recommended).
From the pit of water, head straight up the stairs, down the hall, and up the spiral staircase back to the entrance of the instance.
Main area Edit
This is the primary section of the temple, and the place where the boss for the achievement is located. There are many bosses you have to go through before you reach the final one (Zul'Lor, Gasher, Loro, Zolo, Mijan, Hukku, Zekkis, Veyzhak the Cannibal, Kazkaz the Unholy, Jammal'an the Prophet, and Ogom the Wretched, Dreamscythe and Weaver, Hazzas and Morphaz, Shade of Eranikus, and the optional Avatar of Hakkar), and trash mobs that vary in difficulty (some can CC you with sleep or fear, both magic debuffs that can be dispelled by priests, paladins, or Resto shamans).
From the entrance to the instance there are two passageways (facing away from the portal, take either passage ahead of you), either one is fine as they both lead to the same place (just remember to go up the stairs first). Once up the stairs you can either go left or right, it doesn't matter, just stick to one direction. Along this circular hallway there will be several mobs, most commonly consisting of a large troll zombie (tank), a priest and/or bloodrinker (healer), and two imps (non-elites). Send an off-tank to attack the healer and the main tank to their tank (remember that you can probably CC one or more of the enemies in each group). At intervals you will see stone blocks with masks on them; these masks mean that if you go down it will lead you to a Protector (one of the six that protect the final bosses of the instance). Most of the protectors are very easy to kill, and will on occasion give some loot (BOP greens). When a mask leads you down stairs on the outside of the ring, clear the mobs at the landing, and then take the hallway on that floor (do not continue down the stairs). After defeating a protector in a location like that, head back up the way you came and continue around the circular hallway in the direct you previously were. Once you have cleared all six protectors, Jammal'an the Prophet will yell that the shield is broken. This begins the second part of the main instance.
Once you kill the final troll protector, jump off of the balcony as a group, preferably tank first. Be ready to fight a group of dragons immediately. Leaving ranged AOE and heals on top of the balcony while fighting is not a good idea, because if anyone pulls aggro, the mobs may rush off towards the stairs and pull additional enemies. Once down, you'll notice that in the center of the room there is a hole. This hole is directly above the shallow pool of water where Atal'alarion appears. Do not fall into the hole. You will end up taking a lot of time trying to get back up, but you will probably die (especially if you are not a mage or priest with the ability to float). If you ever want to go through the hole, make sure you have a party member cast Slow Fall or Levitate on you before you fall (note that you will probably float to one side of the ring, and potentially pull aggro from whatever mob is standing there).
Before seeking out Jammal'an the Prophet, you should understand that if you do not kill every dragon whelp and dragonkin in the instance (the guys on this floor), they will attack you during the fight with Shade of Eranikus. It is possible to kill the boss before they arrive to help, however your group will definitely be killed when they arrive.
Jammal'an the Prophet Edit
From this point, there are three major and four minor bosses left to be killed. One of the three majors, Avatar of Hakkar, is completely optional and requires a chain quest to be completed (starting with  ). The boss order is pretty linear, with Avatar of Hakkar available to be defeated at any time. Linearly, first you should start with Jammal'an the Prophet. You can reach him by heading through the southeastern passage of the room (it curves northward into a room of pews). There are at least 7 groups of mobs in the area that you must eliminate. Each group primarily consists of a healer and two undead warriors (CC-able) that must be pulled back to the corner because they can fear you into other groups. This fear is a magic debuff and can be dispelled, and Undead can use Will of the Forsaken to get out of it quickly. Each of these mobs, when killed, will create an aggressive spirit that is immune to all damage and abilities; however each will die automatically after about 30 seconds.
After you have cleared the entire room of mobs, you can take on Jammal'an the Prophet (level 50) and Ogom the Wretched (level 49). Jammal'an is pretty simple to kill but will take a while. Melee DPS or an off-tank should pick off Ogom while the main tank keeps Jammal'an on them the entire time. Kill Jammal'an first, as he has the ability to turn one party member against the rest. After killing both of them, go back out to the center ring and you will see Dreamscythe and Weaver flying around.
The Dreamer Edit
To awaken the final boss, you'll have to defeat his children, four large green dragons (it is technically possible to attack the Shade without killing these four, but most normal groups will want to kill them first.) First, take out Dreamscythe and Weaver, pulling them back to a spot away from other dragonkin and safely away from the center hole. Keep these drakes turned away from the group, as they have acid spit that can spread across all five members. If you off-tank one drake, keep it turned to one side, away from the main tank and the rest of the group. Kill Dreamscythe first, and then Weaver. These mobs only sometimes drop loot, but can be skinned 100% of the time.
Shade of Eranikus is located in the hallway to the south, protected by two more large drakes. Before you head that way, make sure you kill all of the mobs in the center area, and the ones hidden in the small tunnel in front of the staircase back to the entrance (located to the north). There are no dragonkin located in the western hallways, only wind serpents.
Head to the southern tunnel, and clear out the mobs until you can see Hazzas and Morphaz flying around. Once ready, pull them back into the hallway, and once again split the dragons up and turn them. These two have the ability to knockback players, so tank them with your back to the wall.
You've finally made it to the Shade of Eranikus, who is sitting alone in a large room. If you didn't clear the entire floor of dragonkin, they will begin running to attack you once you pull Shade. Simply tank Shade like any other dragon, to one side so melee DPS is standing at his stomach and ranged is safely away from his face and tail. This is a long fight so have buffs and heals ready. A priest's Lightwell is extremely useful here. Once Eranikus dies he will give the Essence of Eranikus which begins and finishes a quest in the room, rewarding everyone with the Chained Essence of Eranikus. After finishing Shade, unless you can face the Avatar of Hakkar, your only choice is to go somewhere else. You can either run back to the center area and up the stairs to the north, fall down the pit in the center safely (with slow fall or levitate), or hearth.