thi is only a funny aproach
"luchar a brazo partido" lit, "to fight with broken-arm-style" -->"luchar hasta que te partan el brazo"/fight till one's (or someone's else) arm is broken--> "go all out/take it to the max/exert maximum effort"
Saludos
PD I have found the real answer. I was not so bad
Do you know why “LUCHAR A BRAZO PARTIDO ” is
done without weapons, but
nevertheless it measures fierceness and
perseverence?.
The expression is compatible to "NO DAR EL BRAZO A TORCER"
Both have their origin in a custom that consists of
determing who
has stronger
arm mucles. The right hands grasped mutually and the elbows supported in a rigid surface.
In such competition, the contenders the own force and persistence are measured, not their weapons.
The loser ends
up with the “partido” arm, with "partido" meaning "broken, fallen, loser".
Sorry for the translation