This depends on which Batman we mean.Originally Posted by The_Glyphstone
The campy, 1960s Batman is immune to anything serious, which puts Cthulu at a serious disadvantage. Campy Batman wins. ;D
The psychopathicBatmanMary Sue who gloated over strangling Superman has already been converted by Cthulu, so there's no fight--Cthulu long ago tookBatmanMary Sue's soul.
The real Batman recognizes that he's totally outclassed by a god, and calls in the Justice League, which collectively can beat Cthulu, driving him back into the insane reaches whence he came (for now--MUhaha!;D)