In recent times, people have started using the word beast as a verb (i.e., beast it, you've got to beast harder).
Is there any information about when this trend started and how it came about?
It appears it is used mainly as military slang and in football.
to beast verb:
to beast — vb:
to beast it (slang)
The only evidence I can find in Ngram shows a very limited use of the expressions you mentioned. Hope other users can produce more evidence on this.
The OED entry for beast as a verb was last updated in 1887, but both of the senses they list are related to the military slang meaning “punishment/forfeit through arduous exercise” (which isn't listed explicitly). The citations are surprisingly early.
OED insists on documentary evidence of how a word has been used, which can make slang difficult to date. Slang might be expected to be first written long after it entered the language in speech. Beast as military slang has definitely appeared in print recently, but probably hadn’t before 1887. A Google Ngram search for