Wonderful mash-up of “right between the eyes” and “on the nose”, both referring to exactitude. Facial features seem to be popular in malaphors….also expressions using animals.
If you type this malaphor on a google search, you get hundreds of responses, reflecting how often this malaphor is written/spoken. It is a blend of “hit it on the nose” and “hit the nail on the head”, both phrases meaning getting something exactly right. I suspect the confusion here is also prompted by two words that are both body parts and four letter words. It also could be from watching too many Three Stooges comedies.