The game was designed so you could view your achievements in the Game Center app. However Apple has removed the app a while back. It seems they are not really interested in the feature any more.
Presumably they expect the game to show you your achievements, but as I'm the only programmer on the team (of two

), I just don't have the time, sorry. The Quest will not receive any new updates, apart from fixes for critical bugs. And new expansions, of course, if/when they are created.
(Seeing how they handle these things, I'm not entirely sure we'll add achivements to The Quest 2 on iOS, but we'll see.)