A backstabbing boss is a nightmare.
As others have said, good record keeping is absolutely essential - I used to make detailed notes of meetings with my backstabbing boss which were filed on the relelvent files in the same way as meetings with the client or third parties were (not foll proof, but hard to eradicate completely)
I also found (with a boss who wouldn't respond / male decisions) that an e-mail that said in effect "This is what I intend to do unless I hear from you that you want me to do something different by [time]" was useful.
Also, stay very calm and professional (my backstabbing boss would lie about whether he had been consulted / what he had said , and would also bully people until they snapped and shouted back at them, and would then discipline them as if they had shouted at him unprovoked...
Unless you have supportive management and colleagues the only way to deal is to find a different job, unfortunately. Sadly, this kind of person often has a non-existant, or uninterested boss who is not prepared to address the problem (When I left the job I had with a back-stabbing boss, I wrote to the senior partner explaining why I had left, how this person had treated me and other members of staff. I never received a response, or even any acknowledement. They were not interested at all in how that part of the business was being run.