This glitched for me as well! I started this game a couple years ago and quit playing it because it was really not much fun. I just started it back up and finished collecting all the mini-kits and the achievement did not unlock.
Can anyone tell me about how much time we are talking about to redo all the stories and recollect all the mini-kits (by starting a new save)?
According to the in-game clock, I have played over 43 hours and still haven't done the assault missions. This is definitely the worst, longest, and most tedious LEGO game of them all.