Shanghai to Huangshan, you could take the bus at the long-distance south bus station which takes about 5 hrs by costing around CNY135 per person; from Huangshan to Zhuzhou, it seems there are no buses. You would better choose to take a train such as K155 to Zhuzhou; From Zhuzhou to Zhangjiajie, you could take the bus at the bus station on Zuanshi Road. It will costs around 5hrs with ticket price of about CNY100.

Zhangjiajie to Guilin, there are no direct trains. You can take the direct buses provided by some local travel agencies. From Guilin to Kunming and Kunming to Shangri-la, you would better take flight, as it is too toilsome taking bus more than 20hrs.