I tried deleting my save data to reset achievements and progress, and start afresh.
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However, the game's "My Pet Dungeon" is still showing full achievements and every stage already unlocked.

Apparently, deleting my save data didn't actually delete anything?

Where can I find my real save data so I can delete it and therefore all of the "My Pet Dungeon" progress?

Will I need to uninstall/reinstall the entire game?

I figured out the problem, I had to de-activate the cloud save syncing.

It's still showing the achievements, but at least the "My Pet Dungeon" progress has been reset so I can experience it all over again.

Not sure how to de-question this thread, though. It seems I can't mark my own reply as a solution.