My download was stuck at 53% for a while... What I did was go into the "My Games and Apps" app, and went down to the Queue, where I could see the Destiny Beta download progress. With the Destiny Beta selected, press the menu button (used to be start). Select "Pause installation". After the installation pauses, press the menu button again, and select "Resume installation". It may still say paused for a few moments, before it resumes downloading.