Well, I think this has been suggested before, after going through the S&S. This would make us more like the other sites and unoriginal. Also, AP isn't too important, it's just a nice addition to an amazing site. Besides, there are plenty of ways to get AP already if you are too concerned about it, just try not to spam to gain Armorpoints.
There is an achievement system, when you write good reviews on games, if the review is good enough, you could receive a merit. A merit is worth 25AP, and they are a reward. As the definition for achievement is the action of accomplishing something So by you going out there, writing a good review on a game, and if you do receive a merit, congratulations you accomplished something, therefore you have made and achievement. Now the definition of system is "interacting artifacts designed to work as a coherent entity," which means when a mod merits a comment made by us users, that is a system. To some it up, AG has a Achievement System.
I sincerely doubt we'll get another form of achievement system, but either way it has been suggested before, and ArmorGames is aware that some people want it.