Although some details are still under wraps about the Xbox One, Microsoft did share a few details about the achievement system, saying that the system has had some fundamental changes to the way it works and how players interact with their achievements.
Unlike with the Xbox 360, achievements won't be tied down to games, and whilst there are likely to be game-specific achievements, it sounds as if you'll be able to progress with achievements across multiple games.
It could be possible that some games can contribute to achievements like '1,000 total headshots' but I can imagine most of these achievements to be things like '50 total hours played' or '25 games played.'
Players will also be able to upload and share footage of their games and achievement progress, similarly to the PlayStation 4's new share feature that was revealed earlier this year.
Currently details are a bit sparse, but it's likely we'll hear more about the new dynamic achievement system soon.