I'm also having trouble unlocking the achievements. I played through the game in offline mode. When I came online, none of the achievements registered, so I tried playing through again while online, but most of the achievements never triggered. I think I only got the one where you don't meet mustache girl in the first level and the one where you equip 3 badges. A bit if a bummer since I'm a completionist and I really like A Hat in Time.