If there were achievement badges they would appear on your BeamNG.com profile, and other people could see them. It would be cool to have them in the game because there would be tricks you have to do to get them. Here's an example of one: Tree Hugger. Crash into a tree 10 times. Tell me what you think about this idea!
As we all know, everyone loves achievements. Heck even random software now has achievements (on steam), so I think that this is a decent idea. I guess I'll contribute another one... (I think that this one will be hard to get for most players XD) Safe Driver: Drive 10 miles without hitting anything.
This would never really work unless/until BeamNG gets turned into more of a "game" where there is actually an objective and a goal.
Wouldn't the game then have to have some type of online feature in order to have the achievments linked to your account on the forums? I suppose it could write them to a file in which could be linked to your profile but it seems that could be modified by the user to add achievments in which one has not earned