Try FLAG_SECURE:
public class FlagSecureTestActivity extends Activity {
@Override
public void onCreate(Bundle savedInstanceState) {
super.onCreate(savedInstanceState);
getWindow().setFlags(WindowManager.LayoutParams.FLAG_SECURE,
WindowManager.LayoutParams.FLAG_SECURE);
setContentView(R.layout.main);
}
}
This definitely secures against manual screenshots and automatic screenshots from the ICS recent-tasks history. It also secures against screen recording (e.g., apps using the media projection APIs).
UPDATE: it also secures against Now On Tap or other assistants on Android 6.0; they will not get access to the details of widgets and containers in your UI if the user brings up the assistant.
UPDATE #2: however, not everything in the activity will be protected. Any pop-up windows — Dialog, Spinner, AutoCompleteTextView, action bar overflow, etc. — will be insecure. You can fix the Dialog problem by calling getWindow() on it and setting FLAG_SECURE. The rest... gets tricky. See this blog post for more.