Resolved as duplicate. Use https://bugs.mojang.com/browse/MCPE-10840 for tracking purposes.
Affected as well. I created a thread on TA on August 5th which is a few days after I noticed they stopped unlocking.
http://www.trueachievements.com/forum/viewthread.aspx?tid=825798&anchor=6496946#m6496946
You can see from my personal history I unlocked DIAMONDS! on August 2nd while playing a local LAN game with my daughter on her tablet.
http://www.trueachievements.com/Minecraft-Pocket-Edition-iOS/achievements.htm?gamerid=287004
I was unable to unlock any achievements after that for several days. I tried every day until I randomly earned The Lie on August 10th, but since then no other achievements have unlocked despite quite clearly meeting the requirements. I have not noticed these issues in any other platform that I have MCPE on (Google Play, Amazon App Store, etc)
For those with the issue I have been able to unlock achievements again but logging out and logging back in to my Xbox account from the main menu. Try that and see if that helps.