Not a documentary, but you could try the 1997 MLB All Star Game. The Big Cat had a great season at first base that year. I'm sure the Detroit Tigers had a representative too.
On a serious note, this is pretty good. Tiger: Spy in the Jungle http://animal.discovery.com/tv/tiger-spy-jungle/
You'll find a bunch online at ninjavideo.net ... http://www.ninjavideo.net/cat/591 BBC "Tiger - Spy in the Jungle" .... This is a great documentary if you can get your hands on it, best one I've ever seen about big cats.