Many thanks to those betta enthusiasts who have put their efforts to develop halfmoon for many decades. Now almost every one can breed halfmoon, but still there are many points we should develop.
First is the caudal that is very long and large. Some or most of halfmoon can not hold it when they are old. Halfmoon caudal is very delicated to water condition, to temperature, to exercise and many many more.
The second point is the dorsal. Dorsal start to droop down from top when they are not even 4 months old. (see pic below left) May be, as some said, because of the strenght of the rays.