I struggled on this bit, i asked for help and i got past it on the first try, so heres my advice:
Always stay on the right side of the wagon.
You dont need to worry about the monsters, just use your gale boomerang to blow out the cart.
Z target the bird, then just keep pressing B repeatidly with your bow out(dont use bomb combo, they miss because they slow it down) - remeber therer is still another bird in the next area.
If you ever miss the bird or dont kill it, while going round in the circle just try take out the monsters with slash or spin attack.
Hope this helped!