I think it's really unfair on students that there is this substantial difference between A Level and undergrad, which so many of them don't seem prepared for. And when I talk to teachers, they find it annoying too
Yes, yes, indeed.
Things for your DD to think past: the emphasis on the "right" answer. My undergrads are always on about this, and it drives me crazy. It comes from the ridiculousness of targets and league tables for schools at A Levels, and teachers teaching to the test. It cripples bright undergrads.
But I know that teachers are questioned and undermined if they don't get the results - or rather if their pupils don't get the "right" results. The crumbing of a world-class education system, unfortunately.
So your DD should be ready to entertain uncertainty, complexity, and blurred areas - grey areas of critical opinion, and to strike the words "right" or "correct" words out of her critical vocabulary. She should eschew the very typical A level exam/essay writing technique of collecting "quotes" THEY'RE QUOTATIONS from various critics and then patching them together into what they think is an essay. It's not.
Reading, and understanding that her point of view is important - "situating oneself" - in relation to the ways a text can be interpreted, and the ways it can make meaning.
Understanding that "point of view" is not subjective, but that objectivity is not possible; that an interpretation is valid if it is argued for, with valid, analytical, independent evidence, drawn from close reading and analysis of primary texts, combined with an understanding of context.
With Eagleton, she'll get a kind of soft Marxisim, which is very readable, and very engaged with the power of texts not just to represent the world from which they emerge, but also to construct and structure the reader's world-view. That is, fictions not just mirrors of their world, but active world-makers.
Peter Barry's book is a great text book, and cover a number of different theoretical approaches.