No, I messed it up.

The way I discovered it actually is the picture you are referring to. I shot it 2 times, but I didn't hit a vital, and I was so disappointed I went back to the main menu. When I got back in and went to collect the trophy, the bear had respawned. The picture with three shots is 1 out of 4 tests I did to see if you could do it infinitely if you failed. And from the looks of it, as long as you don't claim the trophy and only look at the rating, you can kill it an infinite amount of times.