There are 2 archmages, and they're both seperate bosses, so you can technically get this boss twice.
All characters must have underwater breathing or bubble cluster on as both of these bosses are located under water; faeries must have both affects. Be sure to wear these affects prior to entering the water.
One is in Aequtus, which pops randomly in the area. He is trackable, if alive, and can be almost anywhere. The area is almost entirely NPK with some intermittent CPK.
From the entrance of Atlantis, go down, and east. Follow this east path through a CPK room, into an NPK tunnel. Travel down a few rooms, scanning for the Archmage. Do not go in the room below the Archmage, as it is a death trap. This area is full of somewhat hard-hitting aggro mobs, so this can be fairly challenging for non-hero characters.
An Archmage of Fire Encounter
Decent AR and underwater breathing / bubble cluster is a must. Upon entering his room, you may get aggro'd by other NPCs. Simply calm, and attack the archmage. You may want to calm and cast dispel magic on him several times to get rid of his Sanc and Haste (this makes the fight much easier). Simply spell him up as normal (ff, curse/condemn, plague, poison, slow, weaken, etc) and whittle him down with melee damage. Keep yourself healed up, and flee UP if you need to get out quickly, but be careful of the aggros that surround him.
Keep an eye on "who underw" while fighting him. If another archon whom you do not know shows up, it is better to simply flee down into the DT than attempt to try to get out back through the CPK. This is a very silly mistake that many players make.