Here is the Niggun of the Besht that was in the last episode of Srugim, as performed by the young women of Ulpanat ha-Rav Baharan. (hat tip via FB) Here is a version with a faster tempo that has a very different feel than the clip below.
Interestingly, there seems to be some dispute about the identity of the Nigun Ha-Besht. The tune that’s most often called “Adam Ha-Rishon’s Nigun” is also variously called “Nigun Ha-Besht”. Heichal HaNegina has a post about the latter tune where he refers to the fact that it’s known as Nigun Ha-Besht: http://heichalhanegina.blogspot.com/2007/11/setting-record-straight.html