Irregular

Note: '''It is assumed for now that an Irregular forces open the doors of the Tower in order to enter the Inner Tower. It is unknown who or what teleports them into the Tower or even how teleportation functions outside of the Tower. This assumption that "Irregulars forcefully enter the Tower" will remain in its current form until more evidence appears to support or disprove it. '''

It is also unknown exactly what qualities are required to enter the Tower apart from possessing inner strength like determination, perseverance, bravery in the face of danger, etc. 

An Irregular is a being that has forcefully entered the Tower without being chosen. However, Headon told Rachel that "you're not the person the Tower has selected" and "you have not been chosen".(Ch 76) So it is very likely this is a definition used by the Zahard Empire as in ancient times, people like Zahard and 10 Great Warriors entered The Tower because they had the qualities to do so and were thus, chosen by The Tower. There was no such thing as "chosen Regulars" then.

All the known Irregulars that have entered the Tower are famous for being extremely powerful, and have wreaked havoc and terror within the Tower. Their mysterious ability to control and manipulate Shinsoo exceptionally well is also deemed abnormal by the residents of the tower, as Irregulars are capable of having more freedom in controlling Shinsoo even with the restrictions imposed by the laws of the Tower. It is interesting to note that all known Irregulars that have become Rankers have surpassed every single active High Ranker in just one act, Phantaminum storming Zahard's palace, Enryu killing a Guardian, Urek Mazino fighting toe to toe with Arie Hon then being deemed stronger by the latter. It is also interesting to note that none of the known Irregulars have the same position, possibly hinting at the creation of an elite team that could reach the top of the Tower.

Note: Under the current testing system established by the Zahard Empire, the key difference between Regulars and Irregulars is this. Regulars are chosen by Headon and then, instantly teleported to the Second Floor. However, Irregulars simply force open the door of the Tower and are then, teleported to the First Floor to take the Guardian's test (conducted by Headon). That is: they are "unchosen".

Zahard & 10 Great Familes
Although King Zahard and the 10 Great Warriors came into the Tower from the outside world in ancient times, this was before the testing system was invented. They are not considered as Irregulars because of this. However, they still did force open the door of the Tower.

Known Irregulars

 * Baam (Wave Controller)
 * Phantaminum (Exis)
 * Enryu (Spear Bearer)
 * Urek Mazino (Fisherman)
 * Rachel

Trivia

 * Irregulars aren't all deemed lethally powerful. Such as Rachel. It is just her namesake.