I had heard that you could catch giritina in Distortion World and Turnback Cave in platinum so I think you could catch giritina 2 times
No, you cannot get two Giratina this way. The Giratina in Turnback Cave only appears if you KO'd the Giratina in the Distortion World.
Source: Experience and logic (would they really let you have two Giratina?)
You can only get Giratina in Distortion World but if you kill it, it will reappear in Turnback Cave.Giratina is levl 47.
Source: http://www.serebii.net/platinum/legends.shtml