Trial of Fire
The Trial of Fire is where players complete the quest and can earn the achievement. It can be accessed by flying mount or by selecting the fire stone and teleporting here from the Arcane Pinnacle.
According to the warning emotes provided in the quest:
Every few seconds, many of the nearby runes will burst with fire.
As each rune bursts, a bolt of fire will travel to one or more nearby runes, triggering it to be one of the next runes to burst.
If you watch these bolts of fire closely to see which runes are not hit, you can spot safe spots for the next burst.
Stay within the runes without getting hit by fire until you have 10 stacks of Fire Dancing to complete the trial.
In addition to Image of Archmage Xylem, an apprentice named Darwin can be found here attempting to perform the trial and dancing. You can follow Darwin's movements in order to accomplish it. Although the description calls it a fire dance you don't have to dance.