PLEASE CLOSE and/or merge with other reports of specific achievements not working.  I was able to trigger Treasure Hunter [Bedrock Only], so bedrock-specific is not a relevant factor.

[Original Text]

Since updating to the Bedrock edition on PlayStation 4, the trophy list has been expanded to show Bedrock-specific (labelled [Bedrock only]) achievements, but fulfilling the requirements are not triggering them.  Finding and opening a buried treasure chest does not register Me Gold! Pushing and pulling a piston with a sticky piston does not register Inception. 

Single-player survival, newly created world. Non-Bedrock-specific achievements (Plethora of Cats and Where Have you Been?) appear to work correctly.