While Rorschach is admittedly a sick bastard, as well as tough as nails, resourceful, mean and ballsy... Batman is highly... HIGHLY trained as a fighter.
The fact that "no gadgets" is even brought in as a factor is even worse for Rorschach because now he has no tricks to pull as game changers and even with them he would be dead in minutes.
Batman wins this fight with both hands behind his back and a blindfold on... Rorschach doesn't stand a chance.
Rorschach is completely undisciplined while Batman is all anout discipline this would be an easy flight for Batman.
Batman would make Ror look like a baby... I mean come on, his training alone makes it a joke to compare the two, let alone his experience! I mean he has been fighting since like 1939 and Ror has only been fighting crime since the mid 80s.
Batman 'nuff said
Batman would out think Rorsach and beat his ass using his own shoe to do it with. Rorschach VS Punisher maybe, both has average intelligence and compareable physicall stats and fight dirty.
Super man vs Dr. Mahanttan? ummm no. Manhattan is pretty much unstoppable against anyone or thing. Dr could turn superman into plain ol man or plain ol kryptonic jelly.
Rorschach is resourceful and while he stinks he still knows how to handle himself. He's smart, quick, agile and bloody mean. No Robin could handle him. No way.
Batman on the other hand, would be able to subdue him pretty quickly. Batman once kicked Superman's ass. (I know, he used tech but still, Superman of all people!)
So yeah, Batman would clean his clock if Rorschach made him mad enough.
Now, Ozymandius, that was a great suggestion....