https://www.quora.com/What-is-the-origin-of-the-term-batshit-crazy#:~:text=I can fi-,It comes from a popular phrase from around the turn,batty” to “batshit”.
A person who is batshit crazy is considered certifiably nuts. The phrase had origins in the old fashioned term " bats in the belfrey." Old fashioned churches had a structure at the top called a belfrey, which housed the church bells. Bats are highly sensitive to sounds and would not inhabit any belfry of an active church where the bell was being rung often. When a church became abandoned and many years would pass without the bell being rung, bats would eventually inhabit the belfry. So, when somebody said that an individual had "bats in the belfry" it meant that there was "nothing going on upstairs" (as in that person's brain). So to be batshit is to take this a step further. A person who is batshit crazy is so nuts that not only is their belfry full of bats, but there are so many bats that have been there for so long that the belfry is coated in batshit. Therefore, the craziest of the crazy people are considered BATSHIT CRAZY.