EDIT- This Achievement seems to have been fixed somehow and my guess would be a Hot Patch. The best way to get it to unlock seems to be either just simply loading up the game, loading a old save, pulling up the achievement list for the game which personally worked for myself, and some have reported it randomly popping while playing other games. All I can say is thank you to everyone who took the time to submit tickets, and gaining the momentum we needed to get this fixed. I can't say for certain that 2K was indeed the cause of the fix, but it seems highly likely due to the amount of people that all unlocked it around the same time.
THIS IS NOT A GUIDE, But a fellow warning!
This achievement has totally glitched for me and I can't unlock it no matter what I do!
I have unlocked the achievement for inventing 100 items which is really ticking me off to add to it. I have tried reverting saves, hard resetting my console, deleting my profile off my Xbox and recovering it, and saying a prayer to the Bioshock Gods and nothing has worked!
As soon as I noticed that my tracker was putting progress towards inventing 100 items/inventing every type of ammo, and I hadn't yet unlocked this achievement first I immediately started to worry and tried doing every fix I knew but still no luck.
If ANYONE has experienced this glitch and has fixed please let me know your method ASAP. I'm sorry if this isn't the place to put this, but I felt other people should know it could happen to them as well.
Also I should add, I was not "cheating/glitching/farming" items, etc. in any type of way and was playing completely normal and nothing out of the ordinary.
I should also add that I have not tried to see if the achievement will unlock if I start a new game and make it to where I can invent something and see. Also, I even reverted a save and did not invent anything until *spoiler* the mandatory item you have to invent in the farmers market.