Prerequisites for Baby Rudin
Solution 1:
I'm currently going through Baby Rudin myself. So far, I've found it challenging in a good way, and haven't had problems understanding things, except for a couple of theorems whose proofs were a little to terse for my skill level. Gladly, I wasn't the only one who had this problem, and was able to find questions here asking for clarification of said proofs.
In my opinion, the most important prerequisite for Baby Rudin is a good understanding of logic and of how to derive knowledge from the axiomatic method, i.e., how to write and read proofs. You should know how to prove a conjunction, disjunction, implication and biconditional, how to use contrapositives, direct and indirect proofs and, of course, induction. I think knowing all this is extremely important if you want to understand the proofs and where they come from.
If you don't have a good grasp on how to prove things, I strongly recommend you read the first part of this Proof, Logic, and Conjecture: The Mathematician's Toolbox . It pertains to logic and how to write and understand proofs. It helped me tremendously.