It's colloquial/slang to use 'was beat' instead of 'was beaten.' Another colloquial aspect of that sentence is "so bad"...correct would be "so badly." It's not technically correct, but it is a common colloquialism. It's common enough that it's not surprising you would see it in a book.

Alex, "Some of her kinfolks didn't know her,she was beat so bad." When the Midwest of the U.S. was settled in the 19th century many of the newly formed communities did not have the same educational opportunities that existed back in the Eastern States. The result was that a non-standard English developed, particularly in the Southern Midwestern states. In those states many of the irregual verbs forms changed: Ex. eat, ate, eaten....................became..... eat, ate, ate swim, swam, swum............became.......swim, swam, swam choose, chose, chosen.....became.......choose, chose, chose. ...and so forth. So in the Midwest, in the past, it was not uncommon to hear, We have chose this church for the wedding. The man was beat so bad. He actually has swam across the river. So the dialogue that you listened to was probably real Midwestern American speech. That is the way many people talked in the past. In fact, you can still hear it today. It may be not be grammatically correct, but it is authentic.

James, you are sorely mistaken! 'badly' is an adverb, meaning it modifies a verb. So "beaten badly" means the beating was not done properly! LOL. Therefore, "was beaten so bad" is correct. And 'badly' is wholly incorrect.