There is a way to one-bird it. I haven't played that level in a while and just tried it again but only succeeded with two birds and about 71k. My high score on that level is over 76k, so it must be a one-bird.

If I remember correctly, the spot is just under the bricks. You can hit the bricks and tip it over, but you want just one of them to go over the edge and the other two straight down. Then your bird has to roll just right to take out the two pillars.