Examples of Batman showcasing his quick sharp mind or cleverness to defeat or outsmart his enemies/opponents on the spot
Figures out that the device Prankster is about to use (a device the villain just used to shrink Superman) could be dangerous, somehow prevents it from working and quickly takes out Prankster with a well-placed batarang (Superman Batman #57)
Planning to find out what the Suicide Squad is hiding in the infirmary of Blackgate prison (where he infiltrated into), Bats pretends that the injures he sustained in his clash against Zsasz were worse than they actually were, by slipping into a trance-like state similar to coma, so he is brought where he wanted to be. Then, he slips out of his trance to continue his investigation (Gotham Underground #4)
Superman Batman #48
After easily taking out Hotshot (soldier specially trained in aerial combat with high tech weaponry to take out Superman), he talks Brannon (Hotshot's boss and leader of a team assembled by Amanda Waller to stop the Man Of Steel) into helping him stop All American Boy (a soldier turned into a kryptonite-fueled Doomsday clone who is beating Supes black and blue)
Then raids Waller's computers to find evidence against her and All-American Boy's weakness. Thus, he arrives just in time to save Superman with his high tech Batplane, slowing down the monster just long enough for Brannon to bring his parents to him, therefore stopping his rampage.
Finally, Bats uses the dirt he got on Waller to "persuade" her to stop pursing Superman and himself, gets her to hand over all the kryptonite she has stored away, and rebuild Smallville after the destructive battle between All American Boy and Superman
Tricks Ra's Al Ghul into revealing to him the real importance of a globe The Demon's Head used to own & ended up in the British museum, where it was stolen from, and takes a photo of a map of all the Lazarus pits present in the world (Detective Comics #840)
Tricks the Key into trapping himself inside an inescapable trap of his own doing exploiting his fetish for escaping impossible traps and using it against him (Gotham Knights #5)
Cleverly tricks Lex Luthor into revealing that he has a private lab without initially knowing for sure (Justice League v2 #35)
Bats is prisoner of 2 of Darkseid's evil gods, unconscious and enveloped by the Lump, who is also hiding in Batman's memories disguised as Alfred and triggering the dark Knight's recollections. Lump is a telepathic parasite whose purpose is to sample Bruce genetic material and duplicate his memories, in order to create an army of clones each as good and as driven as Bats, but under Darkseid's control.
Batman first notices that the "Alfred" in his memories isn't really Alfred and that something is amiss, thus forcing the evil gods to have the Lump create false memories to distract the Dark Knight Detective:
Then he somehow senses the evil gods and changes the false memories the Lump is creating, thus forcing the evil gods to stop using them
After some time, while the evil gods are noticing that giving Batman's memories to his clones isn't such a good idea, after all, Bats confronts in his mind and exposes the Lump
Finally, when the Lump tries to subdue Bats with the Caped Crusader's own memories, Batman resists the assault, gives him a concentrate dose of memories that causes the clones to try and kill themselves and when the evil gods choose to terminate the Lump to break the connection and salvage what's left of the clones, Bruce convinces a dying Lump to help him escape
Tricks Metron (New God of knowledge & science) into transforming himself into a human being in order to get the New God to become vulnerable so he could easily knock Metron out with 1 punch then doses the New God with hypnotic agent. In doing so, he's able to save his JLA team mates (Arthur, Kyle Rayner, and Wally West) from being stuck in the future who rightfully are returned to the past and later recall the events that took place (JLA #14)
Faces Kryppen, an Arkham inmate who is specialized in poisons and has struck a deal with Neron (at the time the top Devil-type of the DCU, excluding Lucifer & Fallen One of Vertigo lore). Kryppen has poisoned all the Arkham residents (guards and inmates alike) and wanted Batman to kill any of the Arkham people in exchange for the antidote. In this way, Bats would have lost his soul to Neron, who would have returned Kryppen the favour by making him ruler of the world. But the Dark Knight refuses the deal and outsmarts Kryppen (and, indirectly, Neron) by poisoning him with his own venom & making him realize that he can't be the ruler of the world if he dies, thus forcing him to hand Bats the antidote without a life being taken (Batman: Devil's Asylum, part of the "Underworld Unleashed" crossover)
Using his own righteous anger against him, Batman tricks the Spectre into breaking his own impenetrable sphere that the Spirit of Vengeance has imprisoned the JLA within. However in order for the plan to work, Bruce ultimately has to sacrifice himself (with Superman willingly joining him) in the process so the rest of his team mates can escape and continue on with the mission (DC 2000 #1-2)
Superman: Man Of Steel #105
Joker tricked Mister Mxyptlk into giving him more than 90% of the imp's power, remade the universe in his own image, defeated everybody who opposed him (Batman and Superman among them), destroyed & recreated the universe effortlessly and has just put Supes through an horrible life designed to break him, with Bats forced to watch. The Man Of Steel managed to not break by causing his own death. Taking advantage of this and despite having gone through many gruesome deaths and resurrection (among other things) has left him in a bad shape, the Dark Knight masterfully manages to manipulate the now near omnipotent killer clown into bringing back from the dead Superman and put him through another dose of nightmarish reality, this time including Lois. This ultimately causes Superman to break Emperor Joker's hold over him, as expected by Bats and unforeseen by the clown, leading also the JLAers to awaken.