Hi,
as Grant086 stated in his solution, this boss fight is quite tricky and it comes down to trial and error. At least in the racing phases.
For the fighting phases I found a strategy that worked perfectly for me. Here is what I did:
I jumped into the middle part of the arena. There, I let myself fall to the ground and started building blocks from the bottom to the top which just enough space for me to jump between them. You can imagine it as a kind of vertical ladder, built out of 5 blocks.
Then I made my way to the top of this "ladder". Standing there you just need to fall down from one block to the other to avoid the small birds.
After the last small bird you need to be quick though, since the fat bird will be heading directly towards you.
If you need additional help in the racing parts of this stage, or if you don't like the ladder method, you can also watch the video below.
( video credits: Plagueis Xboxlivefr)
I hope this helps you guys :-)
Any improvements? Please let me know in the comments below!