I just like to tell you my experience, I had exact same experience as you with my boss in current job, what I did is I set meetings with my boss and my boss's boss to discuss my situation and my boss's evaluation on me, express the great job you've done, tell the truth the boss's boss did not know, ... but you must keep calm down and be objective..., in the first 6 month my boss even expended my probation period one more month, and two month ago she gave me another writing warning because of one small issue, but after I addressed my opinion and the reason to my boss's boss, and he trusted me after I explained everything. at least my boss seems nice to me.
Anyway, that's my story and take care.