What is the proper way to get a manager fired?

We have a horrible manager at our center who has been there for a while. She wont get promoted cause the higher ups cant stand her, shes basically a glorified pencil pusher to get the reload shift done. Miraculously the weeks shes on vacation we have zero drama and get done an hour or two earlier. Constant favoritism, only writes up who she doesnt like, doesnt care about anyones wishes or concerns, just overall a very toxic person to run our shift. A number of us employees are planning on going to HR with our steward to write statements to hopefully get her removed, but id like to know from you guys if theres anything else we need to do.