Well, many sites have them... There could be a part inside the profile with the deviant's achievements, things like 100 deviations uploaded, 10000 pageviews reached, 50 critiques given, 500 comments given, things like that. I hope this doesn't sound too silly. n.nU
And yeah, it would just encourage more people to fake or alter those. You can submit 100 deviations and all of them are one line drawn in muro. You can send 100 comments that are all 'asdf'. You can get bots to raise your pageviews. Etc.
The problem with that is, as soon as you add an "achievement" for something, people start doing it only to get the achievement. Or it would seem that way to everyone else. Instead of commenting on art because, you know, it's good to leave feedback on people's art, people would be leaving comments to unlock some stupid and meaningless achievement. And no one wants that.
I would argue that the badges we have are already achievements. But then I don't ever use sites that have achievements, so I don't know.
This sounds interesting, but in reality it would probably only encourage pointless spamming than anything else. What works on one site isn't always suitable to use on another. Leave the achievements and trophies to the gamers.