Echoes of Doomfire

No convoluted strategy needed, wait for Doomfire (giant green ball) and kill the boss. That's it.

Ok i just got the achievement on US-Frostmourne...We misunderstood the whole achievement thanks to blizzard which resulted in a few wipes..Here is whats confirmed.
1:You dont need Doomfire Spirit alive during the entire fight.meaning ? u can kill the Doomfire spirits (one that spawns the fire)
2:Push the boss to 45% and wait for the Allure to pop
3:Nuke the boss down under 2 minutes Right after the Allure is cast. Reason to do so is that the fire from allure disappears after 2 minutes.so the main objective is to dps as hard as you can when the boss is below 40%.
4: If the Allure is cast at 42-45% you only need to check the Nether Banish..Make sure boss dies 10-15 seconds before 3rd Nether portal spawns.Cos every nether portal has 1 minute cooldown.Hope this helped :)

Happy raiding.

Another way of doing this achievement is simply outgearing the fight (think 710+ average ilvl, normal difficulty) and burning the boss like you'd normally do, we had a 4:35 kill which resulted in us getting the achievement without trying for it!
With lower ilvls it might be worth saving the last doomfire spirit for 20 or 30 seconds when you push the boss just to be safe.