Most likely originating in some elementary school, or possible middle, somewhere in the southern U.S. as that is where it is generally used. (Mostly by kids. Or immature teens like yours truly.)
1. Completely awesome; amazing
Example: "I saw a horror movie today. It was totally beast-mode."
2. Powerful; amazingly strong; rivaling Superman
Example: "Have you seen the new quarterback for LSU? He's beast-mode."
Beast-mode can also be shortened to "beast" if needed.
Example: "I love myself! I'm so beast!"
In addition, "beast" can be used as a verb rather than an adjective.
1. To be awesome; to be, well, beast-mode
Example: "Did you see that? I totally beasted out there.