beat (one's) brains out

1. To put forth one's maximum effort, especially for some activity that is or proves to be futile or unproductive. I've been beating my brains out trying to get a passing grade this semester, so failing by two measly points is incredibly frustrating. Don't beat your brains out trying to please these people—they'll never appreciate it. What am I going to do? I beat my brains out all morning and still can't remember what the password is!

2. To physically attack one, as with punches and other blows, such that they suffer significant injury. This phrase can be used both literally and hyperbolically. I'm worried that the captain of the football team will beat my brains out if he finds out that I'm secretly seeing his girlfriend. As if I didn't feel bad enough after losing the case, my boss beat my brains out for it once I got back to the office. If you ever scare me like that again, I'll beat your brains out, I swear!

beat one's brains (out), to

A more colloquial version of cudgel one’s brains or rack one’s brain, meaning, like them, to strain to remember something or solve a difficult problem. It dates from the sixteenth century, when Christopher Marlowe wrote, “Guise beats his brains to catch us in his trap” (The Massacre of Paris, 1593, 1.1).