I was in a very similar position. It's not possible to unseat the bird (it just goes back to that block). The only way to beat it is to do a cartwheel. Stretch up and on your way down, use your left hand to grab the ring below. Keep tensed and relax when your character is to the right of the ring, then loosen to gain momentum from the swing. When your character is almost inverted, release and extend your right hand to the ring that is an "I" in your case. From there, you can either swat the bird and use that momentum to get to the next ring or just go for the one of the left.
Actually I managed to do it the way Mot22 is (apparently) trying to do it. After many tries, I was able to kick the bird away, swing away, swing back and grab the ring where the bird was with my left hand. Quite a stretch.
I was in a very similar position. It's not possible to unseat the bird (it just goes back to that block). The only way to beat it is to do a cartwheel. Stretch up and on your way down, use your left hand to grab the ring below. Keep tensed and relax when your character is to the right of the ring, then loosen to gain momentum from the swing. When your character is almost inverted, release and extend your right hand to the ring that is an "I" in your case. From there, you can either swat the bird and use that momentum to get to the next ring or just go for the one of the left.
Actually I managed to do it the way Mot22 is (apparently) trying to do it. After many tries, I was able to kick the bird away, swing away, swing back and grab the ring where the bird was with my left hand. Quite a stretch.