* The Will of the Abyss is more of a force of nature than a human being, more or a what than a who. She is something of a paradox; ancient yet childlike, regal yet immature, bitter yet innocent, powerful yet vulnerable, wise in some aspects and entirely clueless in others. She tends to function by her own logic and rules. She is amoral, psychopathic: everything she does stems from her own whims and desires, and she tends to believe only what she wants to believe.
* She has spent the past century as the queen of her own dark and twisted kingdom, her only company Chains, memories, and those poor unfortunates who are dragged down into the Abyss by the weight of their misdeeds. This has left her spoiled, insane, and really not much of a people-person. Underneath this, however, she is very very lonely, and desperate to be loved.
* She detests her sister. She considers herself to be the real Alice. (When she speaks to people she introduces herself as such. The Will of the Abyss would be more of a title.) Her twin was only a vessel, and now not even that. Hence her jealous rage, when Oz chose B-Rabbit over her.
* She is very possessive of Jack Vessalius and will endeavor to harm or outright kill anyone who seems as though they might come between her and him. Any and all Vincents and Glens (possibly even Lacies, if she's feeling especially unstable that day) are particularly likely to be tormented by her, if she has the chance, though she isn't fond of Gilbert either. (He's much too close to her beloved Jack.)
*As Jack is the most precious person to her in the world, she will go out of her way to please him. Oz, occupying his body as he is, will gain a fair amount of her favor as well, particularly if he treats her nicely.
* She is the daughter of Lacie and Glen (Levi) Baskerville, and niece of Glen (Oswald).
* As the Will of the Abyss, the bulk of her power extends over things and creatures of it. As such, Chains in particular might want to be wary of her and/or court her favor (Apart from Hatter, perhaps. Hatter tops everyone). This is not, however, to say that she is not a danger to humans. She is fast, indifferent to pain, and prone to violence when it suits her. Take care, or you might find yourself missing and eye. ;-)
As the vessel for the Core of the Abyss, she also likely retains some of that ability to breathe life into inanimate things, be it a doll or a dead body...