Yay! We have an achievements dialog: http://meta.stackexchange.com/questions/220429

As previously part of that request, but now split off to its own (as requested by Arie on the linked post) is overlays on the achievements icon:

![enter image description here][1]

similar to on the desktop, and as done for the app inbox


  [1]: https://i.sstatic.net/8KznP.png