beat one's brains out meaning

or beat one's brains out
To puzzle about something
[American idiom]
to work very hard (to do something). (Informal or slang.)
• I beat my brains out to solve the problem.
• That's the last time I'll beat my brains out trying to cook a nice dinner for you.
[American slang]
to try very hard to do something.
  If you think I'm going to beat my brains out to do this, you are crazy.
  I beat out my brains to do this for you!
  I won't beat my brains out again for you!