Hello! I would have given you all my notes on this but annoyingly I deleted them all just last week! I'll tell you what I can remember anyway.
First of all, and I know this might sound obvious, the textbook was a life saver. I didn't use it for AS Level but I don't think I would have passed without it in A2. It contains the core of everything you need to know for each of the papers, make sure you go through it thoroughly and take notes.
Another thing that really helped me was reading the Example Candidate Responses that CIE release for the papers. It has examples of band 1-2, 3-4 and 5-6 answers if I remember rightly (basically: brilliant, good and not very good). I only had about 3 weeks to teach myself all of A2 in the end and I'm sure that studying those example answers is what saved me. They come with comments and annotations by the examiners about what works and what doesn't work in an answer (e.g. structure, level of detail, language) so I made note of those things and made sure I paid attention to that in my own answers. My teacher gave me these example responses as I haven't yet found them online so maybe ask your own teacher for them if you don't have them already. It's definelty somthing worth getting hold of.
I also read through almost every exam question that has ever come up to find similarities in what they are looking for. Often it looks like they're asking a really random question but actually, they have just changed the wording to make it look complicated. Nine times out of 10 they're asking exactly the same question as last year (how language is being used to communicate) but just with a different text. Knowing the pattern makes it a bit easier to know what to expect. Xtreme Papers has all of the papers and mark schemes if you're interested.
Again, I know this is a bit obvious, but I think its really important to use some fancy vocabulary in your answers. This is probably most important in creative writing answers but in the A2 papers, it pretty essential to use at least some of the specialized words that are mentioned in the textbook. You want to be able to read the text and then write about the lexis and discourse structure to show that you actually understand what they mean. At first, I made little flashcards with the specialised words on one side and then their definition on the other so I could test myself on them and eventually know what they meant. All that kind of stuff is in the textbook.
For A2 I think what makes you stand out from the crowd is how well you use examples of studies to back up what is being talked about in the text. I did the section on Child Language Aquisition for A2 as I wasn't really interested in the English as a global language section. If you're going to do the same I suggest you look at studies aimed specifically at studies of children in language acquisition (for example, the textbook talks about the study of Genie as proof that there is a critical learning period for children). Again, the textbook does contain quite a few studies on this section but I think if you're aiming for a really good grade you should do your own research and find other examples. You can then use these studies to back up your analysis into the text or use them as a counter-argument to show that you are open to more than just one angle of interpretation.
Sorry for such a long response, I think I got a bit carried away because there seems to be so little information out there on CIE exams! I know a lot of what I've said is quite broad but once you get hold of the example responses and the textbook it should start to make more sense. I hope this helps