Most of the games achievements are obtained through natural story progression with some associated with playing the mini games. You can play the game on casual difficulty but make sure you do not skip the mini games or use hints during your playthrough.
During my playthrough I encountered a problem with unlocking the achievement for beating a hidden object game in under 1 minute. To solve this I quit the game, went into the manage options and deleted my save data for the game and relaunched it. The achievement immediately unlocked on the title screen. If this happens to you wait until you finish the rest of the achievements before using this method.
Here is a full video walkthrough: