The extreme of going apeshit. To completely lose one's mind in a violent manner, or when used to describe a situation, the act of descending into complete chaos.
When I found out that my entire project had been deleted, I went completely apeshit bananas on everyone that had touched my computer in 24 hours.
Drive me bananas = Drive me crazy. It's related to another expression in English: "to go ape" which means to 'go crazy' in the sense of acting 'crazy' like monkeys we see at the zoo act,