When I went to Victoria Falls, I took the train from Dar es Salaam to Zambia (Tanzania-Zambia train, TAZARA for short). The train ride was long (24+ hours), but quite comfortable. I believe from Arusha you can take a bus to Mbeya and get on there and continue to Kapiri Mposhi, Zambia and then take a bus to Livingstone. I know there are also buses that do the same route and I think it takes less time by bus.
However, if you are trying to get there a bit quicker you might have to fly. Personally we enjoyed the train. We got a sleeping room with four beds. There is also a loung car, which was a fun place to drink and talk to Zambians.
We did a cruise on the Zambezi river. It was also great.