beat brains

beat (one's) brains out

1. To put forth one's maximum effort. 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.
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.
See also: beat, brain, out
Farlex Dictionary of Idioms.

beat (one's) brains (out)

Informal To exert or expend great mental effort: She beat her brains out during the examination.
See also: beat, brain
American Heritage® Dictionary of the English Language, Fifth Edition.
See also:
  • beat (one's) brains out
  • beat brains out
  • beat one’s brains out
  • beat one’s brains out to do something
  • beat one's brains out
  • beat someone’s brains out
  • beat your brains out
  • break (one's) back
  • break one's back
  • break your back doing something/to do something
References in periodicals archive
But brawns and intimidating tactics will never beat brains, as I'm sure he'll discover to his cost."
Hotline; EUAN McLEAN ANSWERS YOUR CALLS
Kennedy once said about Bundy, "You can't beat brains," but as Goldstein demonstrates, Bundy was so cerebral he was insensitive to the plight of others, his moral compass so awry at times that it provided no legitimate bearing on which to base policy.
Lessons in Disaster: McGeorge Bundy and the Path to War in Vietnam
How can this be achieved when the beat brains are taken out of poor countries?
Immigration policy without humanity?