Android emulator won't shut down

1. Open Android Studio
2. Go AVD Manager
3. Go Actions Tab
4. Click arrow
5. You will see stop
6. Click and emulator shut down :)

If the device is stopped in a bad state, this may persist when relaunching the emulator. To get around this, simply select 'Cold Boot Now' from the virtual device's drop down menu in the manager.

According to the documentation I found at google, simply closing the emulator window is the correct way to shut the emulator down.

To stop an emulator instance, just close the emulator's window.

Source: Starting and Stopping the Emulator