If its not one that can be bought with gold or bought with feathers then its probably also not 'giftable' by a buddy. A whole month is a real long time to try, something must be wrong. I'd ignore it and work on levels 21-24. The good thing there is that you can win nearly infinite numbers of stars there (up to about 20,000 stars max at a time) from the question mark eggs.
I'd then spend thousands of stars on level 20 for that one last prize.
This is how I finished off all the bonus levels since I'm not going to 'buy' the ability to monkey break there.