The Archmage must have three spell levels in all four of the previous spellcasting classes. The Archmage is also strictly required to win The Destiny Knight, not the least because only an Archmage can become the eponymous Destiny Knight.
A "true" Archmage is a character that has learned all seven levels of spells in all of the other casting classes Conjurer, Magician, Sorcerer and Wizard. In The Destiny Knight and The Thief of Fate, the Archmage is a class of its own, and gain an additional seven levels of spells. FYI: In the second two games, the code for the "Godspell" is ZZGO.
Archmage Development in Tales of the UnknownEdit
In Tales of the Unknown, an Archmage is not a class of its own; it simply refers to a character who has learned all seven levels of spells in the four casting classes. As spellcasting characters can only start in the Conjurer or Magician classes, and both of these classes gain levels faster than the Sorcerer or Wizard classes, you may be best served by following this progression of class changes:
You may be tempted to push one (or both) of your casters through the other starting spellcasting class to have redundancy of spells for your casters (it's nice to be able to have two casters who can cast utility spells like Trap Zap, Ybarra's Mystical Coat of Armor, Kiel's Magic Compass, Major Levitation, Greater Revelation, or Restoration) and to get more spell points/hit points quicker, but in the end game, you'll find that ending your class progression on Conjurer or Magician will get you more spell points and hit points, not to mention increasing the power of spells that are affected by caster level. After Level 13, Conjurers and Magicians level every 230,000 points, compared to 400,000 for Sorcerers and 1,300,000 for Wizards, a difference of 170,000 points for ending on Sorcerer (73% slower!), and a difference of 1,070,000 points for ending on Wizard (465% slower!).
There are two reasons you may want to end up with a Wizard as your final class instead of the faster leveling Magician or Conjurer. 1) The Wizard has some better stats and abilities. Saving throws and spell resists are better. You get more hit points on level up. 2) There are some items later in the game that wizards can wear or use that Conjurers or Magicians can't. Notably the Spectre Snare, Spectre Mace, and certain gloves, shields, helms, staves, and wands.