Arcueid was created by Earth itself as its Ultimate One, is the strongest of the True Ancestors, and a possible vessel for the reincarnation of the Crimson Moon Brunestud, the Ultimate One of the Moon. As the strongest True Ancestor, she also acted as their executioner should they fall prey to their own bloodlust. At this point, she was much like a living god and the strongest non-Servant being in the Nasuverse. She was kept ignorant of her own vampirism, however, and was thus vulnerable to being tricked by Michael Roa Valdamjong into drinking his blood, splitting a large part of her power to him and awakening her own bloodlust.
To control this, she entered periods of extended hibernation, only waking when Roa's soul manifested to try and reclaim her lost power. He has reincarnated 17 times, and his 18th reincarnation brought him to the body of SHIKI Tohno, the adoptive brother of Shiki Tohno. In the Far Side routes, Shiki encounters Arcueid on his way home from school. He stalks her, entering her home and slicing her into 17 pieces. She, unable to heal, uses a majority of her power to create a new body for herself.
She waits for him on his way to school, initially intending to kill him, but ends up wondering what he'd be like instead. She chases him down when he runs, guilting him into helping her track down Roa. They are interrupted by Nrvnqsr Chaos, who hunts them down and forces the weakened Arcueid into a fight. Shiki kills him, and Arcueid decides to reward him by sending a succubus, Len, to give him a dream.
The pair continue hunting down Roa, entering a romantic relationship along the way, and discover his hideout at Shiki's school. Worried for her boyfriend's safety, Arcueid charges in alone, using the last of her power to shred Roa from head to ankle. She dies in Shiki's arms, having used up almost all her life force. After he kills Roa, she uses the portion of her power returned to her to revive, either leaving for her castle to hibernate in her True End or staying with Shiki in her Good End.
Since encountering her completely changes the course of Shiki's life, she doesn't appear in the Near Side Routes at all.
Fate/Shipping Wars (by Leolab)
Combatants: Arata Fukamori & Chris Northfield, Velvet Crowe & Eleanor Hume, Adam and Eve, Wes and Rui, Sypha Belnades (Netflix) & Trevor Belmont (Netflix), Arcueid Brunestud & Shiki Tohno, Ellen Kohagura & Kaoru Mashiko