Batman is not only a world class fighter, he also owns weapons, chemical and biotechnology manufacturing companies. And as a billionaire anything he can't build he can probably buy. He's also paranoid and clever AF and has made multiple contingency plans to take down not only villains but every hero he's come across.
Batman can take down anyone the current writers want him to.
Batman is a genius, in several realms, but as a tactician? MAN.... With time to prepare, including ramming through scientific processes with just fucking CASH, he can probably could take on anyone.
Surprise The Bat? Man, he's fucking solid.... Melee combatant, strategist, understanding of a WIDE field of practices, he is fucking GOOD.
That being said, he is a MAN. Just a human being. GREAT training, GREAT tech, GREAT strategy... but still, something alien to his understanding (not necessarily extra terrestrial in origin) and he gets fucked.
That being said, Batman exemplifies the powers of the human MIND. If we can assess it, HUMANITY can provide a short term solution. Long term, we can fuck ourselves. Short term though? We can kill God, gods, etc.
Batman represents humanity, as a mental construct, at its peak. We can take in, digest, and provide useful solutions to solve a problem. Again, short term. We rarely plan past a generation or two.
Alfred wasn’t one of his trainers. Batman had claimed to have as many as 6 mentors, including Ducard and Ra’s Al Ghul, and Alfred is not on the list.
Take down like kill? No one, that's not Batman's game. Keep someone distracted or incapacitated for a prolonged period, probably quite a few other heroes. In a determined fight to the death with time to prepare, against an opponent who gets the same, a lot less than people like to believe.