I think it's possible but very difficult. You will need to understand basic QFT, quantization of gauge fields, CFTs, and supersymmetry.
That will prepare you to understand, on one side, N=4 super-Yang-Mills theory, which is the boundary CFT in the original version of the correspondence, and on the other side, Type IIB superstring theory with D-branes, which is the theory in the AdS space. String theory is also based on path integrals and CFTs - the "world-sheet" of the string is a 2-dimensional CFT.
But before you get to AdS/CFT, you have to understand that other stuff. Of course you can look ahead to papers on AdS/CFT, and that might help you in deciding where to focus, but the immediate challenge will just be to learn the precursors.
I haven't seen Srednicki and Zee. But for basic QFT, you need to understand how to get "particles" from quantized field modes, and then how to get Feynman diagrams from the perturbation expansion of the S-matrix for weakly interacting fields. You need to be able to switch between the sum-over-histories picture, the state-vector picture of ordinary QM, and the algebra of the perturbation expansion as figured out by Freeman Dyson. I think ideally you'd first do this for a bosonic scalar field theory, to get some intuition and some experience with the formal integrals behind the Feynman diagrams. Then you'd have to plunge into QED, and the new complexities like regularization and renormalization, fermions, and the beginnings of gauge theory. Given your three-month deadline, even with the luckiest decisions about where to focus, I doubt that you have time to become competent with the calculations - there are just too many technical details to learn. So mostly you will have to settle for understanding how it all works.
For gauge theory, the advanced concept that you want is "Faddeev-Popov quantization" or "BRST quantization". Because of the gauge symmetry, formally different histories are physically identical, so you need a way to avoid counting the same physical history twice in the path integral. In BRST you add extra fields, "ghost fields", which vary in a way that counters the redundancy.
Regarding CFTs and renormalization... The modern understanding of renormalization is that you are working with a low-energy approximation to the full field theory, and renormalizability means you can ignore the high-energy behavior even though you don't know what it is. The infinite counterterms which get added to cancel the divergent integrals are just a way of saying "in the real theory, those diagrams get canceled by other diagrams; I don't know the details, but I don't need to know the details". The advanced concept here is "renormalization group flow", and a point of view according to which all QFTs are CFTs with some extra source terms added.
Supersymmetry is less conceptually exotic than all of this - it's just a symmetry connecting fermion fields and boson fields - but it has its own specific algebraic complications, especially "extended supersymmetry" for N>1.
Another semi-technical thing which is relevant for getting to AdS/CFT is the "planar expansion" of QCD for large N (where this N is the number of "colors" in QCD, not the number of "copies of supersymmetry"... this is why the super-N sometimes gets written in a cursive script, to distinguish it). Planar means you only consider Feynman diagrams which can be drawn on the plane without the lines crossing.
When you get closer to learning about CFT, you could try the references in the answers here:
http://physics.stackexchange.com/questions/4743/superconformal-algebra
But first you need to get your basic QFT intuition working.
