Petting Zoo (and other similar pet achievements) don’t have account-wide tracking.
These achievements track the pets that are owned by the character and not those that are in the Pet Journal in the Collections UI.
Were achievements account wide in cata or are they adding them new this time around?
Account-wide achievements were added in MoP.
Currently they are account-wide in Cata Classic but unfortunately they added the old outdated MoP version and not the retail version.