That was Lorraine Crosby, and it is kind of an interesting tale.
https://en.wikipedia.org/wiki/Lorraine_Crosby
She did make great job. They sounded good together
Lorraine was credited as Ms. Loud on the Bat out of Hell II, Back Into Hell. She sang backup on several songs, but was remembered best for her duet in I'd Do Anything For Love, But I Won't Do That.
For the original Bat Out of Hell, Ellen Foley sang the vocals on the album, but didn't want to tour, so Karla DeVito stepped in for the tour. And she's the one most remember from the Bat Out of Hell album videos.