To get strong daora wings, make sure to break the Kushala's wings. You can tell when they're broken as they'll have white chips on them.
To get Jewels, make sure to break the head and sever his tail.
A common tactic is to get the Daora really weak in the first quest, so that you can kill it quickly in the second quest. Save before you go on the second quest, kill it, and reset the PSP if you don't get what you want. You can load up before you went to kill it and try again ;)