Yes but who the hell wants to? Batman is just an Expert 6. All the nameless bad guys are Commoner 1, all the super villains have an extra level or so.
Why NPC levels?
By level 8 a ranger can track a toad over bare stone, while raining, three days afterwards.
By level 8 a rogue can walk across a one inch wide wooden pole, that was dipped in oil.
By level 8 your average sorcerer can convince the queen that the king cheated on her and you are a prince.
By level 8 the wizard disguises him self as Pelor, and the clerics believe it.
By level 8 the bard of convinces the king he cheated on his wife. Then he solves the marital problems afterwards.
By level 8 the fighter can swim. Even with his 50lb armor, 15lb shield, 10lb sword, and 300lbs of stuff on his back.
Batman can't do any of that. His tactic is he pulls a bat anti-whatever out of his ass, uses it, and then throws a few punches. Still not convinced?
He has a crap load of money and gadgets.
So do I, it's called buying a ladder and selling two ten foot poles.
He has suburb combat skills.
Most of the time he fights losers incapable of holding a job and by all rights are locked up in a luny bin instead of a real jail. The few trained people he does go against, Ra's al Ghul for instance are fully capable of beating the hell out of batman if not for some dumb little gadget.
He has awesome detective skills.
Here is a consideration, you have two mental stats, 10 is average in both therefor two 10s = 100IQ. An 16 in wisdom and 14 in intelligence. Your IQ is 150. Don't believe it? Technically speaking, an 18 in wisdom is almost double reasoning & deductive skills of the normal person.
But wait, he is a valuable member of the justice league and it is filled with people with super powers. And he can beat them all!
Dude, Aquaman is considered a valuable member of that team. His abilities include, breathing underwater, talking to fish, and that's it. As impressive as telling a shark to chew on some evil is, it's pretty worthless to a bunch of landwalkers like us. Also have you seen the justice league at all?
Superman: The guy is a dick with an uber weakness to a shiny rock found everywhere.
Wonder Women: Direct deity granted powers that are removed when a man ties her up. Did I mention she loves bondage and gets tied up hourly?
Green Lantern: The guy has a ring that creates whatever he wants, so mostly he makes large hands and crap found in your mom's junk drawer.
Flash: No note of juggernaut powers so his speed don't make him invincible so how does his speedy punches not shatter his fist upon impact with your face? Well I lack a 16 in wisdom, so I don't know how to exploit the basis to that.
Green Arrow: Hahahahahaha this guy is a joke right?
Fine, the justice league is full of idiots. Batman once beat a race of super aliens that took them hostage!
Haven't read that arc. Pretty sure batman pulls a hacking device out of his belt capable of understanding and beating the alien's 16^128 encryption locks at some point though. Someone keeps bluffing Pazuzu for more wishes...
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Now if you want to build a kick ass level 20 D&D character that brings batman's style into play only scaled up to handle fighting things like angelic devas capable of rewriting reality. The Factotum is probably a good place to start.