The first room has a named, Commander Vazkurlack Primescale (100^). Clear the room first. Be wary of some of the droags; they either have a massive knockback or will cast a huge damage spell that may insta-kill you. The warning for the damage spell is a message stating that the air around you grows crisp, and then you'll see a yellow glowing ring on the floor. GET OUT OF THE RING!
Kill the Commander. He has a rare high damage spell called "Primescale" (this dealth 28k damage to us) and will place traps occasionally during the fight (these are like floating landmines, just move out of the way).
Take the southern hallway. This leads to the next named, Frost.
Take the northern hallway. The vigilant constructs along here "rise up" from death and have to be killed twice.
Inside the Sanctum of Fire is Pyre (100^). Clear his room of constructs before engaging him.
During the fight you will receive multiple texts about Pyre. When this occurs a mob will spawn from a column.
Kill the mob that spawns from one of the columns in the room ASAP or he will soon unleash some major damage upon you. Take note that tab targeting doesn't work very well here, so be prepared to turn off autoattack so you can run to the spawns more easily.
Once all four events occur he will be fully weakened and will die.
You may now use the Recall Obelisk in the center of the room to go back to the entrance.
Return to the Commander room and go take the now-open hallway to the east.
Walking through skulls in the middle of the hallway will briefly turn you into an imp and make an extra caretaker spawn.
The next named you encounter is the Eternal Sentinel (102^). Take note that it's not necessary to kill him to complete Shades of Drinal: Puzzle Pieces and from here you can complete the quest without fighting him or The Forgotten Statue. If you have a way past him without aggroing him (I used Soothe as a Templar) you can skip this fight. However, he'll join the fight when The Forgotten Statue comes to life. See the notes below for avoiding the final fight.
Keep him near the gargoyles that are walking around.
Whenever he charges make sure he runs into a gargoyle.
After he hits it 2-3 times it should break and he'll no longer be able to siphon health from it.
If you are using a mercenary, you will have to back it off at times to make him charge you and run over a gargoyle, or it will be impossible to "train" the mob if the merc has aggro on it.
Continue having the Eternal Sentinel charge into the other gargoyles until all four are destroyed.
Continue east. The three injured Draconians will give you hints.
"We were unable to contain the power of the pillars; they cannot be active for long!"
"Should have known... red... counters blue."
"... pedestal... must get the statue on... pedestal."
Next is The Forgotten Statue (102^) in the Forsaken Reliquary. As above, it's not necessary to kill him to complete Shades of Drinal: Puzzle Pieces. Before killing any of the vigilant codexicon in the room, simply charge up to the foot of the statue, grab the map and then get out as fast as you can move. If you can evac, do it. Otherwise, take to your feet. As noted, if you didn't kill Eternal Sentinel he'll come charging down the hall, so use whatever abilities you have to prevent them beating you to death before you can escape.
Before fully clearing the room, play with the pillars to get accustomed to how they function. In a nutshell, the first click makes the red beam appear, the second click makes the blue beam appear, and the third click resets the pillars.
Near the center of the room are four pillars--two red, two blue.
Get the statue to the center pedestal when you need to counter him.
Whenever the statue has a red aura up, counter it with a blue pillar.
Whenever the statue has a blue aura up, counter it with a red pillar.
When dragging him into the aura, make sure he remains there until the message states that his cerulean aura dissipates.
You may now use the Recall Obelisk at the back of the platform to go back to the entrance.