I'm not getting any progress towards any pet battle achievements. Not capturing unique pets, not capturing pets in battle, not winning battles, not capturing pets from certain families, not battling in certain zones..... nothing... none of them are being tallied.
I have noticed the exact same thing. I have captured several new pets in battle tonight, but my achievement progress hasn't budged. I also captured my first rare pet without getting credit, and captured pets aren't counting towards the 'Safari' achievements either.
I was having the same issue- checked the chieves under Pet Battle tabs, and none were being tallied or showing credit. Closed and reloaded my game client, and all are current and accounted for. Odd, but ... yeah :)