“Somebody had to be Bikini Kill,” says a professor in Sini Anderson’s documentary, “or else we all would have starved to death, culturally.” Well, somebody was! And here we are, culturally alive! Sort of. Somebody else had to get it all down in a documentary, and thus The Punk Singer, Anderson’s adoring, all-access biography of original riot grrrl and Bikini Kill frontwoman Kathleen Hanna, that great feminist firebrand who dared to bring women to the front of the mosh pit. Anderson’s movie, like Hanna’s music, is raw and propulsive, anti-indifferent. (And in case any doubt remains, Joan Jett is here to corroborate her greatness.) One memorable story, told early on, is that Hanna’s mom once dropped her from a trust fall on purpose, advising, “Let that be a lesson to you. Don’t trust anyone, not even your own mother.” Really what’s memorable is how she tells it, with compliments to mom’s sadism. Also, this: “What everybody said about us was: We couldn’t play our instruments. And we said: And?” Conscientiously, Anderson gets into how Hanna moved from Bikini Kill to Le Tigre, how she fell for Beastie Boy Adam Horovitz, how Lyme Disease nearly shut her down, and how, still, nothing and no one can shut her up.