Magic Battler of the Dragon Isles

Did not get credit towards this achievement for Setimothes despite defeating with a full team of level 25 magic pets.

Edit: Checked the achievement today after seeing Crysis' reply and I had credit for Setimothes. Seems to be an issue for many/all the pet battle trainers.

Edit #2: It appears this issue has been resolved as of mid-March 2023; I am getting achievement credit immediately after defeating relevant elite pets/pet battlers.

As of 5/10/2023, you do NOT have to have the world quest up for this to count. You just have to beat the trainer with the team. I just completed my entire run and only one of them had the quest. You can complete Family Battler of the Dragon Isles by just meeting the required text of the battle achievements: "Defeat the elite pets and trainers of the Dragon Isles with a team of all level 25 XX pets." (Nothing about the WQ being active.) Hope this helps someone! Have fun!

I also had this happen to me on Arcantus and Swog but after logging out and back into my character the credit appeared for both.