She worked hard for it and got her dream.

She went to war and sacrified her life for her father. I don't really see what the other princesses did to recieve their moments except for believing in themselves.

^Agreed. No one deserves it more. As MissAngelPaws said, she went to war and sacrificed her life, but she also saved the Emeror and all of China from the Huns, a feat well worth recognition.
For me, Tiana and Cinderella were close behind.

and Tiana

It was a tie between Tiana and Cinderella.. they both worked extremely hard and dealing with mean and disgusting people, and also dealing with a death from the most loved ones :'(

They all deserved their moments of happiness because each and every princess worked incredibly hard to overcome the obstacles, achieve their goals or/and fulfill their dreams, however, Cinderella was the one who endured the most of mistreatment and verbal abuse for the most of her young life, the years that were supposed to be the best and most joyful for her ended up being a neverending torment with no relief in sight. When the ball was announced, all she wanted was just one evening for herself and her stepfamily couldn't allow even that because Tremain was afraid it puts her daughters into unadvantageous situation and the only dress Cinderella had - her deseased mother's dress- was ripped to shreds. When she finally got a chance to attend the ball, it was more than she could wish for, but fortunatelly, she ended up finding love and she deserved to get her happily ever after with that man.

Next would be Ariel and Rapunzel, however, I would put the reunion scene between Rapunzel and her parents or the one where Flynn comes back to life instead of the lantern one because those scenes represent a complete freedom and a new start for her as opposed to the lantern scene where she was still living in ignorant bliss believing Gothel is her loving mother.

Ariel!

Her and Mulan for the most. They both have their worst moment before their happy endings.

In my opinion Mulan got much less than she deserved.