Going batty, or acting in a crazy or irrational way, can be described in many different ways. Some synonyms for this phrase might include going insane, losing one's mind, flipping out, or going cuckoo. Other options might include going bonkers, becoming unhinged, or going off the deep end. Still, others might describe this behavior as being mad as a hatter, going postal, or becoming eccentric. Regardless of the particular turn of phrase used to describe this kind of behavior, it's clear that going batty is a common way to convey a sense of craziness or irrationality.