Shiva's Elite are a special group of elite Assassins whom were present with Shiva on Christmas Eve.
A special group of super-elite and powerful assassins in the League of Assassins. Each member was personally handpicked and trained by Shiva herself. Because of their intense training with Shiva, they were considered to be the most feared assassins in the entire League. Their skill was so great, that Talia, and even Ra's were wary of them believing that they would make a dangerous enemy if ever crossed.
Unlike the other members of the League of Assassins who were completely loyal to Talia, Ra's, and their goal of purifying the world, Shiva's Elite were almost uniquely loyal to Shiva, following her every command and going to great lengths to serve her.
Shiva is also apparently more positively inclined and respectful towards her subordinates then Talia or Ra's, as she has never once been seen abusing, ridiculing, executing them or anything of the sort. She also offers to take on opponents who outmatch them personally, which likely contributes to their undivided loyalty and respect to her. She even seems to be inclined to take her subordinates' advice.
Their loyalty is such, that when Shiva eventually left, Shiva's Elites presumably left with her.
Arkham Origins Incident
On the night of Christmas Eve, Shiva's Elite came to Gotham along with Shiva on the orders of Ra's al Ghul. Shiva's Elite, on the orders of Shiva, spent the night capturing and then brutally killing corrupt police officers in an attempt to force Batman out of hiding.
Shiva's Elite fight Batman several times throughout the long night before finally confronting the Dark Knight alongside their mistress in a final confrontation. After Shiva finishes the fight, she along with Shiva's Elite leave Gotham.
After Arkham Origins
What followed between Arkham Origins and Arkham City is unknown. However, it can be assumed that Shiva's Elite left the the League of Assassins with Shiva when she chose to defect as they were not seen.
The members of Shiva's Elite were dressed in similar clothes to the regular Assassins with the addition of longer sleeves, a grey corset, and a red color scheme. They used smoke bombs to perform a teleportation-like move.