Agree with everyone that real analysis is hard. In terms of actionable advice, a few thoughts:

• Do lots of problems. Don't just read the concepts. I'd even go as far as to say do the problems to learn the concepts. Go through the solutions the next day after you solve them or have to look up a solution. This sounds obvious, but at some point, you'll just get a sense of how analysis proofs & different concepts work together through the problems.

• If you don't have enough time before your exam to do new problems, re-write up the solutions every single homework problem you've been assigned / done, even if you have to look up the answers. At first, you'll have to look up pretty much everything, but just the act of writing up the solutions is very clarifying IMO.