Cant spot this achievement on wowhead... and im close to 800 unique pets on live currently.
EDIT 1: You can obtain 704 if not more pets on live without spending a single penny (excluding TCG, CE, Shop, unobtainable pets, etc.)
EDIT 2: On live you can obtain 755/757 (NA/EU). Legion beta added 95 new pets so far, estimated max. number of new pets at the end of Legion is 150+.
EDIT 3: The 300 mount achievement was added in 6.2 - where it was waaaaay harder to achieve 300 mounts vs. 700 pets.
EDIT 4:
https://twitter.com/Muffinus/status/737750767851831296
Q: "Are the battle pets obtained from the Order Halls intended to be non-tradable?"
A: "Yes, hardcore battle pet collectors will need to alt it up to complete their collections."