Concerning Shakespeare's Hamlet, arguing for or against the prompt--Frailty, thy name is not woman--is a bit beside the point. I assume you're asking for evidence that women are not frail in the play, in an attempt to prove Hamlet wrong. One can argue that easy enough: Gertrude is trapped in a man's world and must marry to keep her position in society, and even then her position is not paramount. Claudius clearly rules. This doesn't make her weak, however, it makes a woman's role in a patriarchy weak. One can argue she is pragmatic and practical, not frail.
She repeatedly stands up for her son against Claudius, and walks a line, so to speak, between her husband and her son. Gertrude is gullible, of course, and is duped by Claudius in numerous ways, but that doesn't mean she's frail. And Hamlet even contradicts his own statement later himself, when he says that surely Gertrude didn't marry Claudius for sex, because she is past the age when that is important to women.
But, again, that's a bit beside the point. One can legitimately discuss this issue on two fronts.
First, when Hamlet says that frailty thy name is woman, he is revealing his state of mind. What's at issue is Hamlet's melancholy or depression, and his obsession with his mother's hasty and incestuous remarriage. Hamlet is projecting his personal view of what his mother has done onto his view of all women (this type of projection is a sign of depression). Because his mother is frail, in his view, all women are frail. This is faulty logic, of course, and demonstrates Hamlet's frame of mind. His obsession with his mother's actions are, perhaps, a bit unusual or unnatural. Hamlet has suffered the death of his father and the loss of the throne for himself. Yet, he appears to be bothered much more by his mother's remarriage. His statement that women are frail characterizes Hamlet.
Secondly, one can discuss Hamlet's statement from the veiwpoint of feminism. The issue is: does the play present women in a negative light? Are the women genuine human beings in their own right, or are they only valuable in relation to the men? Answers to these questions and others like them reveal what Elizabethan society's views toward women were--at least in theory and in part. This is a legitimate discussion point concerning Hamlet's statement.
Looking for evidence from female characters in the play that proves Hamlet wrong, though, is not really legitimate. Although the play is not in any way a realistic play (it's written in iambic pentameter, for instance), the characters are complex personalities. Though the play is not realistic, the characters' personalities are lifelike. As such, of course they are frail. Human beings are frail. But they can also be intelligent and creative and greedy and stupid, etc.
In other words, Hamlet's statement doesn't have to be disproved. That's not the issue. Hamlet's state of mind is the issue. But if the characters, including Hamlet, and the play itself, present stereotypical, prejudicial views and depictions, then that can tell readers about Elizabethan's beliefs about women.
For instance, we know today of course that female sex drives do not dissipate as women age, and about that, at least, Hamlet is dead wrong. But you won't find evidence of that in the play.
