What are Viola's characteristics in Twelfth Night?

Viola is passionate and witty, and she is willing to go to great lengths to get what she wants.

Viola is devastated when she learns that her brother drowned.  She doesn’t know what to do or where to go.  She finds out that the Duke of Illyria is interested in a woman named Olivia, and she decides to pretend to be a man to help him.  All of this is pretty extraordinary.  It takes a special kind of woman to pull this off.

Things do not go easily for Viola, even though she is such a convincing young man that no one suspects her secret.  Olivia, the woman she is supposed to convince to fall in love with her new boss Orsino, falls in love with her instead—thinking she is Cesario.  This demonstrates Viola's charisma and intelligence. 

It is her empathy that got her into this position in the first place, and now she is in a bind.  Olivia fell in love with her instead of Orsino.  Viola has some pangs of self-doubt, regretting the deceit of her disguise. 

Disguise, I see, thou art a wickedness,
Wherein the pregnant enemy does much.
How easy is it for the proper-false
In women's waxen hearts to set their forms!
Alas, our frailty is the cause, not we!
For such as we are made of, such we be. (Act 2, Scene 2) 

Although she is basically a good person, deceit is the everyday normal in Viola’s life right now.  In addition to having the problem of Olivia having fallen in love with her because she thinks she is a man named Cesario, Viola has also fallen in love with Orsino.  Orsino suspects nothing, thinking that he can confide in Cesario and trust him. 

At the same time, Viola is a witty young lady.  When Orsino philosophizes that women cannot love equally with men, she speaks up.  She tells him that they can indeed, essentially admitting that she is in love with him but pretending to tell him a story about her “sister.” 

VIOLA

Ay, but I know--

DUKE ORSINO

What dost thou know?

VIOLA

Too well what love women to men may owe:
In faith, they are as true of heart as we.
My father had a daughter loved a man,
As it might be, perhaps, were I a woman,
I should your lordship. (Act 2, Scene 4)

The audience or reader likely finds this conversation very funny, but there is a sadness to it too.  Viola wants to tell Orsino that she loves him, but she has no idea how.  To do so would be to admit she has deceived him this long.  If he rejects her, she will lose him completely.  At least in this position she gets to be close to him and pine for him while he pines for another.

The interaction also shows that Viola is intelligent and witty, despite her harebrained scheme.  She spars verbally with Olivia and with Feste, and here she tells Orsino in no uncertain terms that women can love as deeply as men.  She should know.