I have shot one in Austria some years ago and it was a great moment. You have to leave during the night climbing up the mountains(I was near to my end as we reached), waiting after some hours of climbing for the birds coming with the first light. If there is the right bird (old enough!) you may shoot him with a small bore rifle (.22 Hornet) and you have to hit the small bird well, otherwise you may find only some feathers......
I've got mine and it was a great experience which I will remember till the end of my hunting life. Of course usually you shoot only one or two in your life.

If you ever will have the chance to shoot one in the alps, take it!!!

Best Regards,
Gunwolf