Please try whitelisting files below in your security software and then try retriggering the achievement:
C:\Program Files (x86)\GOG Galaxy\GalaxyClient.exe
C:\Program Files (x86)\GOG Galaxy\GalaxyClientService.exe
C:\ProgramData\GOG.com\Galaxy\redists\GalaxyCommunication.exe
If you still find issues with the GOG Galaxy achievements, please contact us. Make sure to provide the following information: