Lore
Black Iron Tarkus is a mighty knight who helps the Chosen Undead in Sen's Fortress.
Tarkus is most likely another knight from Berenike - the Knights of Berenike were praised for being near-giant in stature, amazingly strong and resilient, but Tarkus was renowned even among his people for his superior strength. He was one of the longest surviving knights to attempt at curing the Curse of the Undead and fulfilling the Prophecy. It is heavily implied that Tarkus is one of the only Undead to complete Sen's Fortress. The area is strewed with hollowed Balder and Berenike knights who were unsuccessful in advancing further.
A corpse, probably his, containing the Black Iron Set and the Black Iron Greatshield can be found near the large painting in Anor Londo. According to the Crestfallen Merchant, Black Iron Tarkus met his doom while attempting to visit Anor Londo. Tarkus paved the way for future the Undead to venture through Anor Londo as he is most likely the one who smashed the glass window that allows players to enter the Painting Hall since the rotating bridge is inaccessible. It is possible that Tarkus fell to his death as his over-encumbrance worked against him.
While not confirmed, his name is likely a nod to Tarkus from Jojo's Bizarre Adventure, who, in order to earn his knighthood, have to overcome the trial of the 77 Rings. Each combatant wears a metal ring and the winner takes the loser's, adding it to his own. They have to defeat 77 opponents, but with each victory, the number of rings they are forced to carry increases.
Theories
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Whilst one may speculate that the knights of Berenike were journeying to Anor Londo to find the fate of the undead, the corpse containing Tarkus's set is located directly outside the Painted World of Ariamis. In addition to this, the Black Iron set boasts the highest fire defence and one of the highest poison resistences in the game. It is possible that Tarkus journeyed to Anor Londo for something in Ariamis, as that's the only part of Anor Londo with fire and poison damage, likely an assassination mission; notable targets would include Precilla or, more likely, King Jeremiah.
When the player intrudes on the Painted World, they are able to fight the phantom of Jeremiah and find his corpse by the exit. It is possible that Tarkus successfully killed Jeremiah in his world, but succumed to his wounds and died in Anor Londo.
Jojo was released in 2012 which is 1 year after the launch of Dark Souls, so the reference sadly can't be true. It could be the other way around though.
JJBA was originally a manga, which began in 1987.