Question

Which archetypal character does Daisy represent in this passage?

It was impossible to regard her as a perfectly well-conducted young lady; she was wanting in a certain indispensable delicacy. It would therefore simplify matters greatly to be able to treat her as the object of one of those sentiments which are called by romancers "lawless passions." That she should seem to wish to get rid of him would help him to think more lightly of her, and to be able to think more lightly of her would make her much less perplexing. But Daisy, on this occasion, continued to present herself as an inscrutable combination of audacity and innocence. 
(from Daisy Miller by Henry James)heroine
free spirit
outcast
virtuous woman

Answer 1

I would say Daisy is presented as a free spirit who didn't conform to society's idea of what a lady should be. The fact that she should be described as being "audacious and innocent" indicates that this is so and also that she did not have "an indispensable delicacy". 

Answer 2

Based on the given passage, the archetypal character Daisy represents is that of a FREE SPIRIT.

She does not fit into a certain mold. She is a contradiction. She have some characteristics of a well-conducted lady but is also found lacking. She is both audacious and innocent at the same time so it is very hard to put her in a box where society can dictate what she should say and do to be acceptable.