I like “it’s a fool’s errand.” (Which comes from the old and cruel tradition of hazing new coworkers by assigning them impossible tasks — buying some blinker fluid, for example.)
There is also “getting blood from stone” or “getting blood from turnip”, used when you are trying to get something from a source that does not supply that thing. “I was trying to get an explanation from Mom, but it’s like getting blood from a turnip.”
Also, “spinning your wheels” (expending a lot of effort without accomplishing anything, a reference to a car with no traction in sand or mud).
For the literary types, you can say “tilting at windmills”, recalling the mad knight Don Quixote “tilting” (attacking with a lance from horseback) against a windmill he believes to be an evil giant, referring to a futile and stupid, but romantic, attempt to accomplish the impossible.
Trying to reverse an irreversible change is “putting toothpaste back in the tube”. Trying to accomplish too much with too limited resources is “putting 10 pounds of crap in a 5-pound bag”.
Seeking help from someone with no power to help you is “talking to the wrong end of the mule” (the joke being that mules are very stubborn and even if you talk to the head-end, the mule will still not cooperate.)