Like a bat out of hell – To move very quickly.
It’s a strange saying when you think about it, I mean, sure a bat would move quickly out of hell, but wouldn’t any animal?
The phrase became popular in the early 1600s, the people of the time believed bats to be related to witches and evil, they believed that they literally lived in hell. The phrase is really just comparing the speed of a thing with something which they knew to move fast – bats. It would compare to today saying ‘like a bat flying about, in its business of being a bat’.