Microsoft has just introduced a plugin to gamify Visual Studio.
See here :
and here :
I reckon this would be a fun thing for IntelliJ to have.
It could also encourage first time users in trying out all that IntelliJ has to offer.
Shouldn't be too hard to do - there already seems to be a bunch of these kinds of stats in the Productivity Guide.
One thing I would suggest though - try to make the achievements things that are actually good and worthwhile.
A lot of the Visual Studio badges are for negative practices.
It would be better to encourage things like making use of refactorings.