To enable achievement notifications, go to “Settings” > “General” and in the “Notifications” section, enable the “When an achievement is unlocked” option:

Also, since Hydra uses the operating system’s native notifications, in order for them to appear while you are playing a game, you need to access the Windows settings and disable these options:

(You need to access the Focus Assist settings if you are using Windows 10, or the equivalent if you are using a Linux distribution)

This way, achievement notifications will appear even if you are playing a game in Full Screen mode.