I wish whoever invented Achievements had done something else instead.
But I saw the remake of Shadow of the Colossus had achievements for killing the colossi, and it really fucks up the mood of the game.
You can apparently disable notifications for achievements on consoles and in Steam, which would potentially help this somewhat if you know to do it beforehand.
Do you have some examples of games that have been made worse by the inclusion of achievements?
Now, in game purchases, on the other hand...