Since this game was made backwards compatibile, and made Game with Gold for the first half of September 2018, I decided to give this achievement another try. Like so many others, I finished this game %100 and got that achievement, but could not get this one to register. I tried multiple times to get it to pop, without success. I believe the best way to get this achievement before was to just play the game and find all the minikits naturally, without using cheats or buying them ahead of time. Now with it being BC and GWG, I downloaded and sat down for an all day marathon. I made sure I loaded my save game file to the cloud from my 360 before loading the game just in case. Upon loading the save file, the achievement popped!
I realize this isn't much of a real solution more than what I did to finally get it to pop after all these years. If you follow CrispyVictim's video, you should now have no trouble getting it!