Everything you've said so far indicates your immediate manager is the problem. Although her boss seems like a dolt too.

Examples:
1) "The deadline was pushed back..." - Hey it happens, but why did the initially-chosen deadline turn out to be unrealistic? Why did the team not meet the deadline? She should not only be able to answer those questions but be willing to take ultimate responsibility for everything happening with her team and her projects.

2) "busy putting out a fire" - In the short-term, maybe not her fault, but as short-term becomes long-term, "fires" become more and more her own fault.

3) Due to the alleged "fire," she didn't show up to the meeting with you and her boss, which is disrespectful to both. Also possibly inefficient (does a manager really need to be the one to personally put out said "fire?"), but that judgment-call depends on the nature of the "fire," which you haven't revealed. Anyway she left you, an individual contributor who is not managing the project, to take criticism about the management of the project. Bad design decisions, often not a management issue, became one when she insisted on hers. Meanwhile, changing requirements, well those are 100% a management problem from the getgo. And the delays. A management problem. Why are you answering for management decisions and management problems? That kind of feedback is normally delivered to someone who has the global big-picture bird's-eye view etc., i.e. the manager. For that matter, just as a matter of protocol, isn't that kind of feedback normally delivered to a direct report rather than two levels down? You said it yourself, "I had no idea..." That's right and why would you? (Well if it was something you should've known, then there was no way for you to know it except by your boss conveying it, so she failed again. Or, it was always her problem to begin with. Either way, she failed.)

4) According to him, you've been screwing up - how would he know that? From her, who has apparently been throwing you under the bus. Like why would you even have been invited to this three-way meeting that really should've been between her & him? Unless she had already started linking the failings (her failings) to you, such that you were an important or even relevant attendee to the meeting. She screws up, she blames you. That's not what a leader does. Meanwhile I bet he's in love with her and finds her blameless in every way. (I'm joking a little bit, but not entirely. Watch them together sometime if you think I'm onto something, and see what you think.)

The thing is, whether any of these points are her fault or not, she is supposed to step up and take responsibility for them and not throw underlings under the bus. That's why she gets the big bucks. If an underling is answering for these things, then WTF put the underling in the manager's chair.

Anyway, based on my reading between the lines of your comments, which I know are only telling your side of the story, I don't think you're going to stay happy in this job. It's going to get more and more shitty, especially if she gets away with it this time. I think you ought to enumerate to the two-levels-up boss all the reasons why you think that whole thing was unfair. Write all the points down on cards if you have to. Stand your ground. He ought to respect your nerve, or if not, if he sees you as a petty threat then you are working for petty people. Hopefully I've given you some perspective or a way of articulating or thinking about things. It's your very first job so you're not as good at spotting this kind of douchebaguerie (Fr.)(JK) or even knowing that it's not normal. Well, strike that, you definitely can tell it's not normal, as your feelings are trying to tell you, so good on ya for listening to them.