Joker: Down in about 30 seconds. Frank would probably try and hose him with automatic fire ("to make sure"), and get sprayed with an acid-squirting flower for getting too close. He'd wise up, get himself a rifle, and leave the smoking, smiling corpse in an alley somewhere.
Riddler: No chance. Frank doesn't play games, and Nigma's death traps or little clues would'nt stop the Punisher. He'd stalk him, stake out his hideout, and bomb it right into Hell.
Catwoman: Where the previous mentioned two were about as vibrant as they come, Catwoman has stealth. She'd get it too close for guns, and Franks' a gunslinger before he's a slugger (not that he doesn't have his share of HtH skills). Frank would beat her into next week, and leave her tied up out in front of a police station somewhere. She's just a theif, not a killer...and a woman; Frank's a bit old-school. I don't think he'd kill Selina.
Two-Face: At this point Frank would've learned the Gotham Rouges aren't the baddies he's used to fighting; they're alot worse. This would be the first real test; Harvey is good with a pistol. In a shoot out, though, he just doesn't have the skill needed to take out The Punisher.
Mr. Freeze: Now we get into an area where Frank might be at a slight disadvantage: metahuman fighting. Freeze's current suit is resistant to all but the highest calibur weapons. This'll probably throw him and cost him a frostbitten limb. However, Frank's a thinker. He learned in the killing fields of Veitnam to stay one step ahead of your enemies. He'd figure out quickly the suit's not just for defense and switch to explosive/incinderary tactics. Another half hour and fighting and fire and heat, and Freeze is dead.
Poison Ivy: Now that Frank knows there's worse out there than Halloween Costumes, he's in full recon mode. Scoping Ivy for days will give him all the information needed. Lacing the water supply for her gardens and personal water with a powerful defoliant, Frank would wait until she was at her weakest, and simply walk up and shotgun blast her into oblivion.
Bane: The problem here is there's finally an opponent for the Punisher that can outfight AND outthink him. Bane would take enough Venom to disarm Frank's arsenel before being inflicted with anything but grazing wounds, and summarily pummeling our dear vigilante into paste. Frank is never without contingincies, and would probably catch Bane off guard whilst he was bragging about how inferior Frank was to him. Probably with a hidden shaped explosive or concealced pistol. Frank's still on a roll, but the wear and tear would start to show _badly_.
Ra's Al Ghul: Now this was what Frank was built for. Deep infiltration of Ra's mansion. Complete dismantling of any defenses or henchmen standing between him and his goal. However, after fighting through Ra's daughter, his personal bodyguard (you remember that bruiser from the cartoon?), and any metahuman mercenaries hired to protect the Demon's Head, Frank would probably have just enough left in him to detonate the explosives he'd hidden during his stealthy entrace. Thus ends the life of Frank Castle and nearly every demon Gotham has to offer, at least in this scenario.
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...Wow, that one kinda got away from me
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and there goes the asylum... 
i mean, make mine marvel?
[ Click to attempt signal recovery... ]
