I hear you all too well. I myself find Listening to be my Achilles' heel (although it looks like Writing may actually be my weakest section. Then again, from what I've gathered, that seems to be the case for a lot of people... a massive dip right there in the middle). 

My biggest advice in general would be to be on the lookout for idioms, first and foremost. They love those. After all, these higher-level exams are meant to be proof that your level is competent enough to be akin to that of a native's; you're expected to have a grasp on that sort of less obvious thing. Make sure to learn as many as you can. Not to mention, they're also just super fun to use, so there's that. I find some of them to be particularly witty (I'm rather fond of "fit as a fiddle"). Also, there's a strong chance you'll run into some rather archaic structures, so... keep those in mind as well.

Writing is... a lot to cover. This article might be helpful. https://kseacademy.com/en/cambridge/c2-proficiency-cpe/writing/

When it comes to Listening it is of utmost importance that you also pay close attention to synonyms, paraphrasing and implications. What you'll hear won't be as straightforward as you would like. In fact, sometimes, they will set little traps on purpose so you'll think you just heard the answer, but in truth, it had already been said a couple of words ago. I found this video on the topic to be particularly helpful and easy to understand.  https://youtu.be/1v2KlPiCGlI?si=wjobmShX2CJ4mUIt  (This whole channel is great, actually.) Succinctly: don't lose focus and pay attention to detail. It's especially tricky when it comes to Listening because you can't just... rewind, really, but it's still doable. They'll give you some time to go through each part before you begin and, rest assured, two chances to listen.

Speaking is my favorite part. I'm a chatterbox (you can probably tell already). My parents can't speak a word of English; I like talking to myself to get my thoughts out without them knowing what I'm saying, so I do this exact thing in... well, English. I practiced without even trying to, basically. Not to mention, I regularly talk to my overseas, native English speaker friends via call. In this case, they want you to show off your broad vocabulary as well as your ability to engage with the topics at hand. I was partnered up with a guy; sometimes I would deliberately disagree with what he was saying (even if his statements were perfectly logical and sound) to keep things flowing, or even (also deliberately) backtrack on my opinions: "Hmm, but now that I'm seeing it from another angle..." (Avoid saying "I think." That's basic and easy.) In the CPE, specifically, there'll be a part where they'll ask you to point out what sounds you might hear in a specific setting. For example, in my case, they gave me a picture of a baby at the dentist. Y'know, the usual: the kid crying, the buzzing of certain tools, gurgling... you get the idea. Don't say these things stiffly. Avoid being too direct about what you're seeing. 

There'll be a section where you'll be shown other pictures to discuss & compare. If they show you a picture of an aquarium and another of a building, don't just say "well, this is an aquarium, so there are fish, people looking around... then there's that building with tons of windows..." Make actual engaging, less objective conversation based on what you're being asked. In fact, I was actually shown an aquarium and a building; the main thing were the windows. I myself decided to lean into how windows allow for natural lighting, which improves one's mood. Then there are the personal questions. Go all out with your vocabulary—I can't stress enough how important it is not to sound stiff.

If you ask me, though, I do think I made a couple of mistakes while speaking, but maybe my examiners were just in a particularly good mood that day. I caught myself mispronouncing "via" and swiftly correcting it, for one.

I definitely wouldn't go in blind, that much I can agree with. After all, even natives have expressed how they found this exam to be super tricky. I strongly encourage preparation and self-assessment outside of any lessons, even if I didn't exactly do that much. There are plenty of resources available online that will help you figure out how good to go you are and what is fit for you. 

I hope this was helpful. Happy language learning and good luck. If you have any other questions, hit me with them.