I still don't think that this kind of information really belongs to a HUD. HUD's are - after all - meant to display only the most crucial information to the player. Information that simply can't be stripped without handicapping the gameplay and/or the player.
But hear me out! I really think that there's a need for the player to be able to see things like kill count and achievment progression - so I think that one cool idea would be to implement a totally new screen (character screen, inventory screen, etc). That screen would perhaps lists all the achievements and the player's progress towards these ones - in-game ofc, and relevant to the current game being played. Many other games have options for displaying achievments in a similiar way. This is just an idea ofc - I'm not the one calling the shots here ^^