beat head against the wall

beat (one's) head against a/the wall

To attempt continuously and fruitlessly to accomplish some task or achieve some goal that is or seems ultimately hopeless. Some people are never going to agree with you on this, so it's no use beating your head against a wall trying to convince everyone. I feel like I've been beating my head against the wall trying to understand this math equation.
See also: beat, head, wall
Farlex Dictionary of Idioms.

beat one's head against the wall

 and bang one's head against a brick wall
Fig. to waste one's time trying hard to accomplish something that is completely hopeless. You're wasting your time trying to figure this puzzle out. You're just beating your head against the wall. You're banging your head against a brick wall trying to get that dog to behave properly.
See also: beat, head, wall
McGraw-Hill Dictionary of American Idioms and Phrasal Verbs.
See also:
  • bang (one's) head into a brick wall
  • beat (one's) head against a/the wall
  • beat one's head against the wall
  • beat (one's) head against a stone wall
  • knock (one's) head against a (brick) wall
  • knock (one's) head against a/the wall
  • knock head against a brick wall
  • bang your head against a brick wall
  • bang (one's) head against a brick wall
  • bang (one's) head against a wall