Having never done an achievements system before, I could do it in what is certainly a very inefficient way. I bet that someone out there knows of a convenient and code-efficient way!
My current system is as follows: I have 16 achievements, each with an icon that is gray if not completed or colored if completed.
In an event, once the player's save file is loaded, I have 16 separate conditions checking to see if each achievement is met. For example, collect X amount of money or play X amount of hours. Once triggered, the achievement sprites have a variable for "IsComplete" that gets turned "true." Any icon that is "IsComplete" changes to its 2nd frame, which is a colored version of the sprite.
If sAchievementIcon.Number = 1 & Hours played >= 50, set "IsComplete" to "true."
If sAchievementIcon.IsComplete = "true," set frame from 0 to 1.
I suppose this could be done in an array, but the conditions for the achievements are not always as simple as "this value is greater than or equal to X." Some achievements involve doing multiple things at once (having a powerup while killing a certain enemy, completing two stages in under 20 seconds, etc), so putting the condition for each achievement in the array is probably more complex than it's worth. So my solution is simply to have 16 separate events that check each time the player's save data is loaded, which seems really inefficient, but is much more user friendly than trying to force unique achievement conditions into arrays.