Mythic Weapons, also known as "The Myriad Arms of Balrahn," are twenty weapons (one for each job) obtained through the "Arms of Balrahn" questline available once you are promoted to Captain Mercenary Rank. In addition, there is a weaponskill associated with each of these, but unlike the Relic weapons' weaponskills, you do not actually need the final Mythic weapon to use them (but you do need the base item from Nyzul Isle Assault).
To begin, you must salvage a base weapon from any Floor of the Nyzul Isle Investigation assault mission, one of which has a chance to drop from any Notorious Monster. With this and a Runic Key, you can have Abquhbah hold on to the weapon as you finish the tasks laid out by Naja Salaheem.
The "Arms of Balrahn" questline is composed of four parts:
These quests involve time-consuming tasks, requiring participation in many activities such as Assault, Salvage, and even Einherjar. The last quest culminates in a battlefield event where the Mythic weapon will "awaken."
The base weapon, the "Nyzul Weapon" can be used to unlock the relic weaponskill by accumulating Weapon Skill Points, the requirement ranging from as high as 16,000 points down to merely 250 points required, depending on which floor of Nyzul Isle is recorded on your Runic Disc when you talk to Zalsuhm with your Nyzul Weapon equipped. See quest Unlocking a Myth. Using the weaponskill with the Mythic Weapon equipped will gain extra effects, referred to as Aftermath.