Q:

Reality Check: Batman

One of the most popular types of superheroes breaks down to the "highly skilled, highly intelligent, (sometimes well funded) martial artist," with the most well known example of this superhero trope being Batman. 
So what is Batman like?
Batman specifically exhibits physical prowess across the board the equal of Olympians, mastery of a variety of martial arts, gymnastic and acrobatic mastery, impressive engineering and craftsmanship skills, hacker/programmer/general computer genius-level capabilities, and ability to buy a wide array of impressive and often military gadgets on a billionaire's budget. He also manages to pull all of this off, fighting crime and supervillians (for the purpose of this question, we'll say "crime, terrorists, and similar threats to American society"). He has a long history of fighting these threats, and has survived the various possibly lethal encounters. And the icing on this cake is that he's accomplished all of this without drawing suspicion from either law enforcement or the public. 
Impressive, but unfortunately unrealistically so.
Within the bounds of:

Human capabilities (mental and physical)
Physics
Economics/Logistics
Criminology
Modern public media
Etc.

And given the constraints/options of:

Our Batman cannot be any richer (liquid and other wealth combined) than any private citizen of the real Earth
Our Batman may be the owner (CEO, President, and primary stockholder) of any one fictitious private business that has a real-life parallel (publicly traded or private).
Our Batman may have mental capabilities of any description as long as there is historic justification for such capabilities
As long as he remains 100% human and bound by biology (or historic examples), his genetics can be whatever makes him best suited for this role
Our Batman works alone or with <5 people (who fulfill secondary or support roles). These people have absolute loyalty, and may hold upto similar physical/mental capabilities as our Batman.
Our Batman must be based out of any one major metropolitan region in the USA.
Our Batman can be of any age that would best fit this role

...How would could such a figure reach the previous listed accomplishments? How far would we have to dial back our caped crusader to return to the realm of reality?

A:

Perhaps not that far at all. Consider in the real world we have seen terrorists like "Carlos the Jackel" capable of committing terrorist attacks against some pretty heavy hitters (like breaking into an OPEC meeting) across the planet without being stopped by police or security services. On the other side, the Mossad sent teams around the world looking for the "Black September" terrorists responsible for planning the 1972 Munich Olympic massacre and were largely successful, also eluding law enforcement and Western security for the most part (Read George Jonas' book "Vengeance" for the account of one of these teams).
Now these people are/were not Olympians, mad scientists, expert computer hackers etc. (Avner, the protagonist and team leader in the book Vengeance describes himself and his team members as presenting like a pretty ordinary bunch of guys). Where they and their opponents are different lies in their mental preparation. In order to work undetected, they need to develop acute powers of observation and memory, have the ability to integrate large quantities of information and make and execute rapid decisions. 
The fact they are/were spies and terrorists means they do have effectively unlimited resources (Spies largely funded by state sponsors. In that period, the USSR, Lybia and other Arab states were sponsors of Terrorism, today we see nations like Iran funnelling billions of dollars to Hezbollah and other proxies, while ISIS was initially funded by the Gulf States as a means of countering Iranian adventurism).
The Israelis going after Black September and Carlos the Jackal are very dated examples, going back to the 1970's. While I have no first hand knowledge, it is quite easy to believe that the training and support that terrorists and spies receive has increased by orders of magnitude since then, and of course the individuals who do these jobs are going to be rated in the sorts of cultures they come from (no spy in the 1970's would be a computer hacker in the sense we understand, since personal computers and the Internet did not exist. Today, however, it would be a rare individual who did not have some knowledge and understanding of computers and the internet).

A:

This reminds me of my inspiration for my protagonist in my novel The Crusader. In the real world, I once worked for a company called Blackwater USA. They were a large government contractor that were responsible for providing security to the State Department and CIA. There was a lot of hype and pandemonium about how Blackwater was a "private army" which was mostly hyperbolic BS, but there is a certain bit of truth at the core. 
The founder of Blackwater is a former Navy SEAL who in the early 2000s ran a significant government contractor which employed a large number of highly trained military vets, owned its own mini "air force", and controlled a pretty respectable arsenal (by corporate, NOT government standards). If you think about this in terms of "real world Batman". Prince was a guy who had some interesting skillsets, would have been capable of self-deploying to pretty much any corner of the world and surviving, had access to a lot of gear and weapons that might be useful, and (had he been so inclined) potentially could have done a lot of the things you would expect of a "real world batman". 
In my novel, I altered some of the background for my protagonist. I went with Delta rather than the SEALs for his background because I felt that the Army SF teams emphasis on counterinsurgency, languages, "force multiplication", and survival training would make him more flexible. Obviously, since I was writing a novel and not a comic book, I gave him some flaws and limitations to make things interesting, but in this case, you could presume that your "batman" is a top-notch specimen probably ex SF or SAS or whatever, who has had some major country spend a few million dollars to train him, and who now controls some sizable corporation. 
To handle the "how does he hide" aspect, I would probably make him a Federal contractor (maybe FBI). That gives him some access to contacts, information, and a certain degree of free movement that would facilitate his vigilantism. Obviously, it goes without saying that any "real world batman" would be always one small step away from a MAJOR prison sentence! Such is the cost of being a superhero though.

A:

If you dialed back Batman to his original appearances, he would easily be a possibility in our world. As he is today, it's still possible, but there are some areas that would need tweaking. 
Human capabilities: This one is easy. Simply look at the peek examples in any given area. 
Starting with mental capabilities, the easiest place to start is IQ. The highest known IQ is around 230, with at least one individual suspected to be in the 250-300 range. So, let's be generous and give Bruce a 300 IQ. That's not the whole picture of a person's mental skills, but it's a quantifiable start. This gives a baseline indicator of verbal, mathematical, spatial and symbolic reasoning, as well as mental processing speed. For someone like Batman, we would probably want to weight the last two categories heavier than the first two, since the ability to identify symbols and patterns, and the general speed of thought would be the most useful to him. 
Beyond that, you have his deductive reasoning, his vast knowledge, his ability to think strategically, and his inventiveness. Again, you can point to real world examples that, when taken together, combine to give a good approximation of Batman's capabilities. Dr. Joseph Bell (the inspiration for Sherlock Holmes) had amazing deductive skills. There are plenty of examples of people with extremely powerful memories. It's a skill that can be learned and practiced. Again, you can point to plenty of examples of master strategists throughout history. I would say this most often comes down to a knowledge (innate or learned) of human behavior, but that's my opinion. Regardless, there are many historical examples of people who were able to defy the odds. And finally, inventiveness. Again, you only need to look at someone like da Vinci to see examples of how creative someone can be. So far, I don't see anything in Batman's mental capabilities that would need to be dialed back.
Physical capabilities again, it's easy to find examples of the peek limits of the human form. Just look at the Guinness Book of World Records. People lifting up to a thousand pounds, breaking several slabs of concrete at once with just their fist, surviving extreme physical trauma, and so on. This might be one area where we would need to dial it down. Not so much in what he can do, but in how much punishment he can take. There are certain laws of physics, and no matter who you are, some of the more comic book-y injuries would simply kill or severely injure you. For example, you can build bone and muscle, but your brain is still a soft mass floating in a small amount of liquid, and a strong enough force is going to cause it to go slamming into your skull with enough force to injure it, no matter who you are. 
Economics: This one is tough. In terms of pure numbers, it's easy. Plenty of places have tried to calculate the real world net worth of various rich superheroes, and Bruce usually comes in at around 10 billion, which is entirely realistic. What is less so is his ability to make that money work as far as building his bat gadgets. Nolan did probably the best job of realistically showing how this could work, but it would still be hard to hide the fact that he's using his money to fund his alter ego. Eventually his shareholders are going to want answers about why they've sunk money into inventing a bunch of prototypes that would have been very successful in military and law enforcement, which went nowhere. 
Social Media: This combined with the technology we have today, would make for the least believable scenario. Cell phone cameras, combined with facial recognition software, and the fact that he's one of the most famous people in the world, would mean someone would put it together sooner or later. Plus there's the fact that few people would have the time and money necessary to put in the training he has and build the gadgets he has. The best way he could accomplish this is with a double - someone close enough in build and features that no one would notice the difference, but they could do the antithesis of the popular shirt "I'm not saying I'm Batman, I'm just saying no one's ever seen me and Batman in the same room together." There, you've seen them in the same room, and you couldn't have two Batmans (Batmen?), so our hero couldn't be Batman. Most likely though, people would still suspect there was at least some connection.
The best option for this is not to be the playboy millionaire, but to be boring. There are enough multi-billionaires that, if he didn't stick out in some way, he could get lost in the crowd. Also, not owning the company that could produce his gear directly would help. If he could figure out some way of getting what he needed covertly from someone else, preferably if they weren't aware, that would further distance himself from a chance to be the Bat. Shell companies, funded through offshore accounts, things like that. 

