Our strategy for Angry Birds Star Wars Cloud City level 4-20 is to send Han straight ahead, blasting the first switch to open the first barrier. Unfortunately, the second barrier is closed by the same switch, so try to get through before it closes. Use Leia to grab the chain boulders, and then Obi-Wan to push blocks into Vader. The score in the video below is 110,010.
PC Bug Alert: There seems to be an issue with PC logging scores on this level, and some of the Boba Fett Missions. For more information, see the v1.2.0 release post.