(Thanks to Fire Emblem Wiki for the following information)

It is speculated that Ursula was one of the original members of the Black Fang, her being one of the legendary Four Fangs and also the only Four Fang specialized in magic. She is known as the Blue Crow amongst the Black Fang members. She is seen to be extremely loyal to the founder of the Black Fang, Brendan Reed, and also shows complete devotion to his wife, Sonia, oblivious to the fact that Sonia was manipulating the Black Fang for her master, Nergal. She is first seen in Chapter 7x of Lyndis's story, where she assigned a Black Fang operative, Beyard, to recapture the children of destiny, Ninian and Nils, and to bring them back to her. 

She is not seen again until the chapter Four Fanged Offense, where the Four Fangs are assigned to kill the lords Eliwood, Hector, and Lyndis, before they could stop Nergal from manipulating the Black Fang gathering more quintessence for Nergal via Bern, although only Nergal and Sonia are aware of this. The Black Fang were merely deluded into thinking that the three lords were corrupt nobles and had to be stopped. Later, she is seen in another chapter, handing the player a Hammerne staff because, despite her orders to kill the Lycian lords or assist any Black Fang members attempting to kill them, she did not want Vaida to accomplish this. 

She is seen in another chapter Battle Before Dawn, where she assigns Jaffar to kill the then Prince Zephiel for King Desmond, and to kill Nino afterward, Sonia finally deeming her worthless. With Nino's intervention, Jaffar is unable to kill either, and Ursula and her assistant, Maxime, along with several Black Fang members, attempt to kill all three. Coincidentally enough, Eliwwod, Hector and Lyndis arrive at the same time, and the three groups clash with one another. Ursula either dies in the battle of fails in killing the lords, Nino, Jaffar, or the prince, and is killed by Limstella for failing in her duties and for extracting for quintessence for Nergal. 

She is seen one last time in Light, a morph resurrected by Nergal's magic with the morph legendary weapon, Excalibur. Upon dying one last time, she dies, finding peace.

Now, for her stats. Ursula is not too difficult to kill in Battle Before Dawn, since she wields rather heavy weapons like Elfire and Bolting, and has low HP despite her other well-balanced stats. In Light, Ursula is quite dangerous, with better stats and an extremely powerful weapon (mentioned above). 

Here are her stats: