1. DVM (obviously) +/- masters +/- PhD
2. Internship
-this can be a LA/SA internship or one specifically for exotics/wildlife
3. Residency in Zoo/wildlife med
That's the more common way to get into the zoo/wildlife niche (again, not always with a masters/PhD), but not all wildlife veterinarians get more formal training past their DVM. I know quite a few that didn't, but have been in wildlife rehab for years. It kind of depends on where exactly you'd like to work, as well. I've noticed that a lot of job postings require the DVM/masters combo, and may say they 'strongly prefer' candidates who are board certified in zoo med. Others are cool if you only have your DVM, but have experience in wildlife medicine. Some require you to be boarded.
http://www.aawv.net/jobs.html#jobs is a good place to see what kind of credentials you might need to get to where you'd like to be.