Magic King

The Magic King is the most powerful magus, typically stated by Lilith to be a level achieved through hard work and effort, however the Magic King candidates have thus far not appeared to follow this principle. There are two known ways to gain the power of a Magic King Candidate: firstly, a person can possess a "Magic King Element" which appears in Liese case as a black jewel and in Hijiri's her entire arm turned black, however she appears to use a jewel similar to Liese Magic King Element to manifest herself in the world, implying that the jewels themselves are the elements. Three magus have been shown with these elements thus far:

Liese: a member of the trinity seven who obtained her Magic King Element from the Eternal Library. her element was "eaten" by Arata and subsequently placed into the care of the Astral Manuscript.

Hijiri: Arata's cousin who obtained her element from the "ruined world", Hijiri appears to be unique, as she actually uses her element to manifest her body in the physical world, she currently resides, and is trapped in, the world outside.

Rogue: Stated to possess a Magic King Element, though the method by which she received it remains unknown.

Abyss Trinity: The Crimson Magic King and Magic King of Luxuria. The father of Lilith Azami. The second known method appears to be possessing the "True Magic King" Astral Trinity, who currently resides inside of Arata. possessing the powers of the True Magic King ultimately appears to be the intended method, as the king shall awaken, join with the trinity seven, destroy the world and then remake it all through this method.

The Magic King Candidates have been shown to possess two highly notable traits: 1. the ability to use multiple archives, as in Arata's case where he can seemingly imitate other people's magic or in Liese where she could steal it from others. Their Theme have been hinted to also play a role in this, as Arata is Rule and Liese is Stagna, the latter's ability to steal other people's magic being a good comparison with her "Sloth" Archieve, as noted by Levi. This perhaps hints that the ability isn't just due to being Magic King Candidates as Rogue and Hijiri have not displayed the ability to employ other people's spells. 2. all of the candidates possess a massive and overwhelming amount of magical power, usually making them highly susceptible to starting Breakdown Phenomenons.

Weakness
The simplest way to kill a magic king is to destroy the magic king element residing inside him.

Trivia

 * In the anime, it is called Demon Lord, rather than Magic King, because both are pronounced "Maou" in Japanese.