I agree with number 5. I have a soft spot for Katherine. I think there is something to be said for all of Shakespeare's women, but if you are talking about a heroine that implies that she is something special and does something heroic.
I'll vote for Katherine in The Taming of the Shrew. She's often seen as just a railing harpy; however, I see her as a complex and reasonable woman. She is dismayed that her father (her only parent) is duped by the false acquiescence of his youngest daughter at her expense. She is outraged at a suitor and husband who treats her abominably. And then she figures it out. She sees through Petruchio's subterfuge and turns the game back on him. The last delightful scene, when the seemingly confident Petruchio is unsure that his wife will come at his beckoning, demonstrates that Kate will have, maybe not the upper hand, but an equal part in this relationship. She will overlook her father's flaws and her husband's motivations and make it work to her benefit. And, what's more, we sense there will be love. I like her!
I agree with #2 - I think to find a truly outstanding heroine you need one who is not a passive character but one who is willing to act and make things happen. So many of the heroines in Shakespeare are very passive characters, whereas we see Portia has pluck, spirit and ingenuity in her ability to deceive both her future husband and society in Venice. The only thing I can't forgive her for is marrying such an idiot as Bassanio! Perhaps beauty is in the eye of the beholder after all...
I like all of the aforementioned characters, but I have to say that my favorite of Shakespeare's heroines is Beatrice. I love her snark and her wit. I know a lot of people see it as if she had gone soft after falling for Benedick, but if you look at it from another point of view, Beatrice is still the same woman she was before she fell in love. In fact, she uses her love to get Benedick to challenge Claudio. It seems more like she's the one in charge. Beatrice is strong, smart, and sharp-witted. I'd love to play her in a play one day.
Yeah, Portia's probably the slickest of Shakespeare's girls. She's a woman of action, always confident, takes the reins and gets things done. I imagine that among actresses Portia's a coveted role.
This is not a question of just one name, basically all shakespearean Comedies' heroins are great because in only such caregory there is scope for heroine. Viola, in Twelfth Night is a good one to consider but she's typical so cannot be great. In my view it may be Portia of The Merchant of Venice, because she is only a centred character that leads a play into success. She solves the problem, she befools people, she is such a figuere in the play that rest characters are very below in male and female in a comparison with her. In the world of this play, Portia is "the sun" that is only seen on the stage and the rest are like stars, that have no significance in the light of that sun. So in this regard Portia is the greatest heroine produced by Shakespeare ever.