If Pell's Gate is visited as instructed in the quest, the Hero of Kvatch will learn that she once lived there as an apprentice to Irroke the Wide. She somehow came across the sword, Umbra, which changed her, making her more aggressive and violent.
She then took the name of the sword and left with a group of mercenaries to sate her blood lust. This evidently didn't work out, and she took up residence in the Vindasel ruin.
Killing Umbra counts as a murder if she is attacked before getting the quest from the Shrine of Clavicus Vile. If the Hero of Kvatch isn't already a member of the Dark Brotherhood, this will get them an invitation.
There is a pillar one can leap onto from the balcony before falling down into the room. Umbra cannot hit the Hero while atop the pillar, preventing her from fighting back. This allows a very low level character to easily kill her with ranged attacks or magic, granted they have enough arrows and are not using the Atronach Birthsign.
If you are a low leveled Argonian, you can lead Umbra into the poison trap nearby,and use paralysis poisons on her until she dies.
For those who have come out of the sewers and gone straight to Vindasel, they will still have Rusty equipment: trying to take her head on will most likely result in death. However, the area she is in is crowded by pillars and altars and she may get stuck behind these if the Hero jumps over them (but only for a couple of seconds). This would be a good time to hit her with some Flares, especially for a Breton or Altmer.
If not much of a ranged fighter or mage, the Goblin's Totem Staff that can be picked up from shamans with 20 pts shock damage does wonders on Umbra when the difficulty is lowered.
To kill Umbra in early stages, one can use a trap in the first room, but it requires many attempts of her being trapped/injured by spikes in order to kill her.
A way to kill Umbra at a very low level, even level one, is to get the mace Rockshatter, which can be acquired by doing the settlement quest When the Vow Breaks, received from Maeva the Buxom at Whitmond Farm just north of Anvil. Don't complete the quest, keep the mace Rockshatter. 5-10 paralysis poisons will also be required which one can purchase, or make. Go to Vindasel and poison her with a paralysis poison while hitting her with Rockshatter, every time a poison runs out apply a new one, continue until Umbra is dead. If done right, Umbra won't be able to make even one hit.
It is also possible to have Umbra chase the Hero back to the Imperial City, and allow the guards to kill her.
In The Elder Scrolls III: Morrowind, Umbra was a powerful orc who wore orcish armor and wielded the same sword with a similar enchantment. It would seem this Orc was also possessed by the sword and that the sword somehow made its way into the the hands of the girl from Pell's Gate in the time between the two games. It also changed from being a two handed to a one handed weapon.
In Latin, the word umbra means shadow. Also whenever there is a solar eclipse in our world the darker part of the shadow in the eclipse is called the "umbra" while the lighter part is called the "penumbra".