First, rather than duel Judai for the Macguffin that can activate his Kill Sat, he holds Edo hostage and forces Judai to trade the Macguffin for his friend's life. Judai then challenges him to a duel, but Saiou points out that now he doesn't have to.
Neos manifests and protects the Macguffin from Saiou, thereby forcing him to duel Judai. During the duel Neos is destroyed, and Saiou sends a Brainwashed minion to activate the Kill Sat while he continues to duel Judai to keep him occupied, using his powers to keep him from fleeing.
As an overall, Saiou has spent the entire season predicting the future and sending minions at Judai, he's realized Judai can Screw Destiny and has defeated every minion thus far despite him predicting Judai will lose. He knows that Judai is the Invincible Hero and thus not only avoided dueling him, but was perfectly aware that if he did duel Judai he would lose, which is precisely why he got the Macguffin another way.
On the other hand, when Judai does indeed trick Saiou into dueling him, he quickly falls for one of The Oldest Tricks in the Book, attacking him out of foolish pride when Judai taunts him, and activating a Trap to destroy his card and summon Neos again. Some people just never learn it seems.
In the next season, Amon realized that Professor Cobra likely had an advantage when it came to dueling, due to the D-Belts, so he tried to subdue the villain mano-a-mano using martial arts. Unfortunately for Amon, Cobra was a former soldier, so he had a big advantage there too.
In Yu-Gi-Oh! The Movie: Pyramid of Light, after Yugi defeats him in a duel, Anubis turns into a monster and decides to skip the card games, attacking his foes directly with intent to kill.
Gin from Detective Conan is this in spades. When one of his colleagues makes a mistake during a Hit (a tabloid photographer took a picture of a scandalous couple embracing, said colleague pointing at the chandelier with his gun was visible in the background) he instantly kills him, not even caring what information he may have about Sherry, a run-away colleague of his... because he already knows she's there, since he heard her panting in the chimney. He then proceeds to head to the roof of the building to catch Sherry, shooting her. And if he ends up getting hit with a tranqualizer? Shoots himself to push the needle out as fast as possible. And although Sherry got away, he knows she'll likely leave the town now that she was found out. (He's out-witted by Conan in this instance since he knows that Gin will think like that and her staying right where she is would be her best bet)
Gin has one instance of his genre-savviness getting the better of him. When he suspects that someone came to the rendevouz place a client had set up, he checks and sees nothing but lockers from a train station... he immediately begins to check them all, but Vodka stops him, saying that no grown person would fit into one of those lockers. Gin agrees, annoyed that he lost his head for a minute and leaves. (Said person was Conan, who fit into the locker decently enough with his child-body)
Roman's Henchmen in Fushigiboshi No Futago Hime. To wit, when Fine and Rein mistook them for working with Eclipse, they overheard them and played along so as to keep the twin princesses' suspicious of Eclipse. Every time they tried to take the Prominence, they would always set up a distraction while the guy holding the machine that would let them take the Prominence hid out of sight and be poised to swipe it; only Eclipse's intervention stopped them from succeeding, though they would always either quickly repair the machine or bring out a replacement. This came to a head when one of them disguised himself as Eclipse and lured Prince Bright into a trap to set up a Hostage For Macguffin situation, where they pulled two sadistic choices in a row, the first to finally gain the Prominence and the second to distract Prince Shade a.k.a. Eclipse and escape. Earlier, another one kidnapped Princess Milky so as to keep Shade away until they had what they needed. This is all despite their goofy (albeit concealed) appearances and mannerisms which would lead viewers to believe them to be little more than a bumbling Goldfish Poop Gang... It appears Roman gave them a proper instruction book.
The Anti-Spiral in Tengen Toppa Gurren Lagann knows that the protagonists gain their power from being Hot-Blooded and through spirit, so they make sure to attack specifically in ways that are designed to break the heroes' morale before destroying them.
Nakago from Fushigi Yuugi often fits this trope. At one point he sends his minions to fend off the heroes who are attempting to keep him and Yui from summoning Seiryu. The heroes beat the minions and battle their way to the top of the tower where the summoning should be taking place—only to find the summoning ritual taking place in another tower not too far away. (Nakago had sent his minions to lure the heroes into climbing the wrong tower.)
Some Mechanical Beasts from Mazinger Z fought dangerously smart. For example, Grengus C3 would lure Mazinger to a lake and then would hit the lake's surface, splashing the cockpit with water and efficiently blinding the pilot -Kouji Kabuto-.
Crocodile captures the heroes in an indestructible cage, rigs the cage to be flooded, and throws away the key, which gets eaten by one of many giant crocodiles in the area. For bonus points, the key thrown away was a fake, and the real one was with Crocodile the entire time. He also anticipates every possible counter to his plans, including taking into account Heroic Sacrifices and such. (And no, he couldn't have just shot them.)
The amazing thing about this plan is it actually had no mistakes in it. The only reason the Straw Hats get out of this is because Crocodile didn't know that there was another pirate in Luffy's crew, Sanji, who would come and break them out of the cell. If Crocodile had known Sanji existed, they would have been doomed. Not only that, he has three layers of plans to kill Luffy. The only reason he fails is because of a massive amount of Plot Armor.
He does it again when fighting the Tsumegeri Guards, four of the greatest warriors in Alabasta. They drank the Hero Water, which gives superhuman strength in exchange for dying five minutes later. You would expect Crocodile to prove that he is the best by showing how easily he could defeat the superhumans, right? Nope, not this guy. He turns himself into sand, flies up on Alabasta palace roof and waits for the water to kill them. It works.
He was also Crazy-Prepared with the bomb he planned to use to blow up Alubarna: In case the bombers were taken out (which happened), the bomb had an automatic timer set to go off anyway. The only reason this failed was because of Pell's Heroic Sacrifice.
Akainu also fits this, emphasis on dangerously. Despite many members of the Whitebeard pirates, Blackbeard pirates, and escaped prisoners in the war being far more powerful and experienced, he nonetheless marks Luffy as the greatest threat due to his "main character" like tendencies, and hounds him above all others.
After the time skip, Sentoumaru notes to himself after hearing reports of the Straw Hats reappearing that they must have become stronger than their last encounter. So he brings with him two Pacifista to investigate, whereas one Pacifista was previously able to curb stomp the entire Straw Hat crew. Luffy, Zoro and Sanji were effortlessly able to destroy the two Pacifista and made their escape. But hey, it was the thought that counts.
When trapped alone on the Thousand Sunny, Caribou, knowing he had no way to take on the entire crew, pretends to be a coward and weakling, while hiding his Logia powers. If it wasn't for Franky catching him, he might have picked off the Straw Hats before the Monster Trio came back.
Smoker, having studied Luffy's personality and habits over the Time Skip due to his obsession with catching him, correctly predicted the island that Luffy was planning on going to first. Its needle was the one shaking most violently, and thus its supposed danger fit Luffy's reckless and adventurous personality. However, Luffy is such a Spanner in the Works that due to a timely distress call and complete happenstance, he ends up going to an island that the log pose didn't even register.
Eneru has a Dangerously Genre Savvy moment when it turns out that Luffy, as a rubber man, is immune to his electricity powers. After a bit of the usual This Cannot Be! reaction (especially when Luffy figures out how to hit him despite his secondary ability to predict attacks,) he finally realizes that he's not immune to indirect uses of his electricity, at which point he uses his electricity to melt some of the gold off his airship, trapping Luffy's arm in a giant ball of molten gold and pushing him off the ship.
Despite being an infamous Idiot Hero Luffy displays an alarming amount of genre savvy from time to time. When Vivi wants to take back her country from Crocodile without anyone dying for it Luffy calls her out on her stupidity, pointing out that sacrifices must always be made, but that it's ok for people like the straw hats (who willingly fight for her) to be the ones. He also tends to make a bee line for the villains of the arc, rightly figuring that as The Hero he's the only one who can beat them. Of course he spends the most of the time being a complete moron so these moments tend to be far and few between.
Trafalgar Law proves to be this during the Punk Hazard arc. Not only does he come up with a plan to force Donflamingo into a Heads I Win, Tails You Lose situation that only failed due to Donflamingo being able to Take a Third Option that no one would see coming, he's smart enough to ally with The Hero to do it. Law also is one of a very few people to not ever underestimate the Straw Hats in any way, even after being subjected to their zaniness, knowing a lot of other big name pirates have and had it bite them in the ass.
Once Law is used to Luffy's tendencies, he realizes that the best thing to do is simply give him a reason to be angry at the desired target and then let Luffy do the rest, as opposed to trying to make Luffy stick to a plan.
During the Inpel Down Arc, Magellan and the rest of the prison staff at least try to be this. For example, Boa is granted access and allowed to talk to Ace, but only after she consents to having her hands shackled with Seastone. (Magellan will not take the risk of someone with Devil Fruit powers getting that close to an important prisoner unless said powers are nullified, even an allies. Nor does he let her talk to him without supervising personally with his leutenents present. (However, Boa is able to deliver a message without him hearing, with some unintended help from Magellan himself; when the other prisoners start making catcalls towards her, Magellan threatens them with his own Devil Fruit powers until them clam up, and with all the screams and shouting, Boa's message is only heard by Ace.)
At the end of Part 3 of JoJo's Bizarre Adventure, Big Bad Dio Brando comes upon Jotaro faking his own death to lure Dio within punching distance. Dio puts an ear to the ground to hear for a heartbeat, though it doesn't work because Jotaro stopped his own heart with Star Platinum to add to the effect. Dio still decides it would be safer to decapitate him from a distance with an uprooted stop sign. This is cranked up even more in the abridged version as Dio even sniffed the air to see if Jotaro was dead.
Dio had his moments in Part 1, too. Knowing that Ripple power was the one thing that could destroy him entirely, he would use his freezing abilities to prevent the heroes from channeling it - pretty quick thinking, too, given that Zeppeli was his first time encountering said powers. Later, having been reduced to just a head, he lured Jonathan down to his coffin and shot him through the throat.
Done again in Part 5 with the White Album fight, in which said power is a suit of ice that protects the User from nearly every type of attack. It has a hole in the back which lets the user breathe but is the only weak spot on it. One of the heroes tries to aim his gun at the hole but not only is stopped due to the villain "Knowing his own power's weakness" but has the bullet shot back at him by "White Album Gently Weeps" which is freezing the air around the villain so nothing can move. And then Mista turns it around by using this to his advantage - he may get hit by the bullets, but Newton's Second Law still applies, and the villain is right in front of a broken lamp post...
And done once more in part 5, where Prosciutto shoots one of the protagonists thrice in the head after dealing a crippling blow him. Mista is saved by his stand catching the bullets for him, though.
Giorno's battle against Cioccolata ended with this. Giorno has inflicted seemingly lethal injuries upon Cioccolata. Knowing that Ciocollata may be Not Quite Dead, Giorno tells him that if he tries anything, Giorno can kill him, but if he doesn't do anything, Giorno will leave him alone. Ciocollata suddenly reveals that while Giorno was talking, Ciocollata used his power to take two of Giorno's friends hostage. Giorno counters by revealing that while he was talking, he was using his power to transform one of the bullets in Ciocollata's skull into a beetle and kill him from the inside out, just in case he was faking being dead.
Kira from Part 4 was genre savvy to the point of paranoia. Then again, it's the primary reason he was able to go 15 years without getting exposed as a Serial Killer.
Throughout Part 3, the main characters immediately assume that anything odd happening around them is the work of an enemy Stand. They're usually right, and the only time that they don't is pretty much one gigantic Idiot Plot.
In Part 2, when Cars fought LisaLisa he had her attack a mook while he sneak attacked her from behind and took her hostage to use against Joseph, while stealing the Red Stone and using the undead army he claimed he wouldn't use against Joseph. Had Stroheim not come, that would have been the end of the series.
Likewise, Itsuki refuses to release Hiei, Kurama, and Kuwabara from the Ura-Otoko. He correctly notes that while they and Yusuke combined could not defeat Sensui at that point, they might be able to escape and eventually increase their strength enough that they could take Sensui on. Which is exactly what they had been counting on.
He also anticipated Ryuk's appearance toward the beginning, killed off every character that posed a threat to him (when he was able) without hesitating, and played up his Faux Affably Evil demeanor to keep most of the taskforce on his side. Also, there's this:
Sympathetic Inspector Antagonist L could qualify too, by immediately deducing that the killings are murder, attempting to invoke and exploit The Power of Friendship with Light, accepting the existence of supernatural forces at play, and outright refusing to accept that Light is not Kira when the circumstances have been set (by Light) to suggest otherwise.
In stark contrast to the game it's based on, villains of the Pokémon Special manga frequently attack the trainer directly. Notably, in Red's battle with Giovanni, the Rocket leader's strategy centered around separating Red from his Poké Balls! The heroes are also willing to use this tactic, so long as the opponent used it first.
Another common tactic in the manga is to destroy the buttons on the Poké Balls, preventing the Pokémon inside from being called out. One memorable moment was when Blaine and Mewtwo used the last bit of their energy to attack Lance's Poké Balls, but it turned out Lance was even more dangerously genre savvy as he already let his Pokémon out beforehand.
After seeing Yellow's powers in action, Storc/Sird wisely decides not to fight her, and later taunts her into using said powers in a non-combat situation to tire her out faster.
A one-off trainer by the name of Katie got into a good bit of this in the anime - rather than sending out Pokémon one by one, her strategy involved swapping them out any time she was up against an obvious type advantage. It doesn't sound like much for anyone who's played the games, but given some of the rule-bending that gets on in the show, it's downright ingenious. It's helped along by Ash deciding not to do this in their battle for no logical reason.
Mewtwo has a Dangerously Genre Savvy moment in Pokémon: The First Movie. When he unleashes his modified Poké Balls to take Ash and friends Pokémon, Ash thinks that if they're already in a Poké Ball, Mewtwo can't take them. Five seconds later, it turns out Mewtwo can, as the modified balls absorb the regular ones, with the Pokémon still inside them.
Team Rocket in the anime has actually gone from ordinary genre savvy villians to this as a result of character development in the Best Wishes arc. After years of facing defeat at the hands of a ten year old and his yellow rat, leaning on the fourth wall, and lampshade hanging, Team Rocket started to avoid involving Pikachu in their plans where possible, and they've actually been much more successful in their exploits because of that.
Brock is prone to hitting on any beautiful woman who crosses his path, especially Nurse Joy and Officer Jenny. When he doesn't hit on them, however, it's a good bet that he knows something is fishy...like Team Rocket using disguises to throw him and his friends off...
Cornelia of Code Geass shows a constant and amazing amount of genre savviness at virtually every turn conceivable. The single best one of these happens to be when V.V. decides to surprise her and attempt to start a bit of a speech up. Not taking any freaking chances, given that she's in the middle of a lair of mind-control-researching wankers, she simply goes for the old school method of saying shut up - knife in the face. (Too bad it didn't take)
From Schneizel knowing well enough to not go to far with his schemes and giving his would be rivals enough ground to keep them from rebelling, to Lelouch's Crazy Preparedness, this show is full of the trope.
Mao thinks he's this and wonders if Lelouch will try to get around his mind-reading powers by launching a robotic attack or lecturing him into submission via videophone. He didn't count on Lelouch doing both simultaneously.
In Claymore, Ophelia backs Clare up against a cliff, cuts off one of her arms, and slashes her across the chest, causing her to plunge into the rushing river far below. She sees Clare reaching for her arm as she falls, though (since she would be able to reattach it), and realizes Clare had chosen that location hoping that she would think that No-One Could Survive That. Naturally, Ophelia is standing there when Clare looks up after making it to shore somewhere downstream.
A bit later, in the War In The North arc, Rigaldo. He doesn't waste any time with introducing himself, instead choosing to simply take the element of surprise, and eliminate the five commanders Veronica, Undine, Jean, Flora and Miria. He succeeds at all of them except Miria.
Makoto Shishio from Rurouni Kenshin is Genre Savvy enough to counteract the most powerful moves of at least three of the strongest fighters in Japan ( Sanosuke, Aoshi and Saitou) and almost do the same with the fourth ( Kenshin).
Digimon Adventure: Our War Game: Diablomon does not fuck around. First, in his initial encounter with the heroes, he skips a level in evolution, tricking them into thinking he was a level weaker than he really was, then he averts Transformation Is a Free Action when they try to match him. Now that he's aware that there are people after him, he calls every single phone number on the planet, clogging up phone lines and disrupting their Internet access and ability to pursue him. When they bypass that with a military satellite uplink, he uses that same uplink to hack the military and lob a nuclear missile in their direction, cutting off the only opposition to him at their source of power. They're still coming after him before the nuke hits, so he then multiplies himself up to a million times and overwhelms them through sheer numbers. Then there's his Batman Gambit in the sequel which tricks the Chosen into enabling him to emerge in the real world. Again, Diablomon does not fuck around.
Normally, one Digimon doesn't launch an attack when the opponent is calling their attack and starts performing it. Angewomon back in Digimon Adventure cut off her opponent midsentence with her own attack on two occasions, once against Big Bad Myotismon and another time against The Dragon and The Rival Lady Devimon. She still calls her own attacks, but she does it fast enough to interrupt them. Both times, this resulted in her scoring the killing blow. Not quite as Dangerously Genre Savvy as Diablomon, but still quite smart.
Apocalymon had traits of this. In his first fight, he was smart enough to attack the children directly, destroy their transformation trinkets, and try and delete them right then and there. The kids managed to counter Genre Savvy him and ride their Digimon the second fight, learning from their previous mistake.
In Heroman, the Skrugg have already demonstrated this trope, not ignoring the heroes, but focusing on them, and improving upon the mechanisms of their army to accommodate fighting the robot the main character has. They also don't shirk off problems, as they stop Will, their currently best soldier, before he does something stupid on the field.
Demon King Piccolo: The first thing he does is have his henchmen go out and kill the world's martial artists, just on the chance that one of them knows the spell that turned him into a Sealed Evil in a Can. When those goons get picked off, he drops what he's doing and goes out to handle the threat personally, giving Goku what might be the most one-sided fight he's had since Taopaipai. He even takes the time to check to see if Goku's pulse has stopped before leaving. The good guys come over to his location and plan to steal the two dragonballs in his dropship, and quickly wish for Shenlong to send him away or destroy him, since at that point, he's the strongest being walking the Earth. Piccolo notices the group has the five remaining balls, so first he walks outside in view with the dragonballs in hand, and swallows them. Meaning the only way they could get them back is if they physically defeat him, which, again, at this point, is nearly impossible. Worse, he comes across the one person who can use the Mafuba (Evil Containment Wave) he fears so much, and he dies in battle, so he easily takes the groups' five dragon balls, summons Shenlong, kills Chaotzu immediately when he tries to make his wish before him, makes his own wish to be restored to his physical prime, and then to top it all off, kill Shenlong so that nothing may ever threaten him. This was probably the bleakest the series had been at that point.
As the saying goes, like father like son. Back when he was still a villain, Piccolo (the second one) fights Goku and eventually leaves him near helpless his entire body crippled save one of his arms. Remembering that Goku was still able to defeat his predecessor with the sole use of his remaining arm, Piccolo proceeds to shoot it out so he can't do the same thing. He would have won were it not for the fact that Goku had the power to fly now and intentionally kept it hidden whole time.
Prior to his battle with Goku, when Piccolo battles Kami and Kami launches the Evil Containment Wave at Piccolo Jr. with the intention of sealing him in a bottle, Piccolo not only reverses the technique and imprison Kami instead but also swallows the bottle that contained Kami during his match with Goku, so that if Goku were to kill him he would end up also killing Kami as well. A leaf straight out of his fathers book.
Frieza also states in the Viz version of the manga that he will rid the universe of all remaining Saiyan blood, and while he constantly insists he doesn't believe in the Super Saiyan legend, it doesn't hurt to be careful.
Jaco the Galactic Patrolman, Dragon Ball Minus and Dragon Ball Z: Battle of Gods/Dragon Ball Super add a few things to this: he did not believe in the slightest in the legends of the Super Saiyan and the Super Saiyan God, but considered about getting rid of the Saiyan in case this time the legends turned out to be true (also implying it's not the first time he destroys a planet because there's a small chance a local legend turned out to be true) and he expects them to rebel; when he finally destroys the planet Vegeta due Beerus asking him to, Frieza makes sure the majority of the Saiyan gets killed by recalling them all and waiting until almost all of them are back, and allows the survival of some of them because the Galactic Patrol has bioweapons that the Saiyan are immune to, thus still having a number of warriors immune to the bioweapon that are now too dependant on him to rebel.
Cell: In his imperfect form, he pulls out extreme amounts of savvy to compensate for the fact that - for the moment - our heroes could still defeat him before he obtained the power he needed, something that sets him apart from many of the other villains in the show (or even himself, come Perfect Form). He rarely gloats and Knows When To Fold 'Em, never brashly fighting in a situation where it would be more cost effective to run instead. He takes advantage of the fact that the heroes can only react to his actions by striking quickly and then leaving before they have time to arrive. He bides his time and acts very patiently, only taking action when he is absolutely sure he can succeed - and when he does fight, he is ruthlessly efficient. Should anyone stand in his way or attack him, he always makes sure to take care of them immediately if he can and do so quickly, rather than let them escape to continue to thwart him later. This becomes especially evident during his initial attempt to absorb 17 and 18: as 16 and Piccolo interrupt him, he stops pursuing his grand goal and takes care of them first, knowing that while he could take the others at his leisure he couldn't allow the only beings nearly as powerful as him to continue to act against him. After he turns Perfect, however, this savvy is slowly edged out in favor of (mostly justified) cockiness - and his ultimate downfall is in part due to losing it all in a fit of smug overconfidence.
Given the above entries for Piccolo, and knowing that Cell has some of Piccolo's DNA inside of him, it shouldn't be a surprise as to where Cell may have gotten this trait. Unfortunately for him, he also has Saiyan DNA, and as he progresses through his forms and gains more strength, more of those Saiyan traits start to come out, overtaking this trope.
Super Buu's surprisingly high intellect and cunning caught a lot of people off-guard in the Buu Arc. Super Buu demanded seeing the "Strong Fighter"/ Gotenks (Goten and Trunks fused together) he was promised by Goku, in an effort to buy more time Piccolo suggests that Buu amuse himself by terrorizing the people of Earth, knowing they can be revived withthe Dragon Balls. Despite Majin Buu previous rampage there were still billions of humans left on earth so Piccolo thought that with that many humans left it would take Super Buu at least a few hours to fly across the world and terrorize every single one of them. Super Buu instead kills every single human, with the exception of Mr Satan, Tien, Chiaotzu and all those present on Kami's Lookout in only two minutes and never left Kami's Lookout while doing it. All of humanity had essentially become a sacrificial lamb for the sake of giving Goten and Trunks just two more minutes of time to train. It's safe to say that Piccolo's plan of trying to outsmart Super Buu to gain more time backfired on him tremendously.
In stark contrast to Cell, he also goes out of his way to prevent his enemies from getting stronger, even when he's sure their boost won't be enough, just to not take chances. He prefers to just straight up kill them. He does this when Gohan and Goku attempt to fuse, and later when Goku and Vegeta attempt the same. "Even if you were to fuse, you would be no threat to me... but why take the chance? I'll just kill you now."
Similar to Freeza, he immediately fires a blast at Dende upon seeing him heal someone.
Future Trunks is a very rare heroic example. He is incredibly more pragmatic than the rest of the heroes. Many of the heroes will hold back for fun, take on enemies for the challenge, or avoid killing. Trunks more often than not goes in with his full power from the start, not giving his enemies a chance to prepare, and goes for the killing blow whenever possible, as early as possible, and does not call his attacks during a fight. He's also the only character in the franchise who ever thinks to attack the villain during his Transformation Sequence (it didn't work, but points for the idea). It's justified when you take his backstory into account, as fighting has always been a matter of life-and-death for him, never for sport.
When Future Trunks set out alongside Krillin to destroy the main timeline's incarnation of Cell and the underground lab, Future Trunks searches the lab prior to destroying it for any leftover data or information about the Androids which could prove vital and uncovers blueprints of Android 17, eventually leading to the discovery of the Android's weakness: a Shut Down Remote.
Kumagawa Misogi from Medaka Box is shown to be this during the Student Council Battle. His involvement in the Manager of General Affairs battle was just to stall Medaka and Hitomi while he had his Minus student council attack Medaka's student council members that were in the middle of training. He didn't care about the outcome because he would have his minions take out the next two participants, essentially giving his side two wins in the process. If they waited until the training finished, he was sure his side would have lost those matches.
Ajimu lives and breathes this trope, to the point where she refuses to fight against the main characters because as soon as she does she'll become the Big Bad, and the Big Bad always loses. Instead, she plots a Hostile Show Takeover, encouraging Zenkichi to win the student council election and dethrone Medaka as the protagonist.
Mermaid Melody Pichi Pichi Pitch: Eriru, despite being quite dumb, is probably the most Genre Savvy of the Dark Lovers. Her schemes are the best at deliberately luring the Mermaid Princesses to her (though catching them is another matter), but her real savvy appears when some event or location is mentioned in an episode, and she always insists on following it up, possibly due to Medium Awareness that if something is mentioned in an episode, it must be important.
Her first appearance showed a twinkle of competence. The princesses attack by singing, so she simply plugged her ears
The fish that were attracted to music.
In Fairy Navigator Runa, the first evil fairy Runa fights exhibits this trope. He attacks her before she's transformed or even knows what's going on, then retreats when Mokke and Senuri show up to fight him.
Mag Mel, the fourth Big Bad of Bakugan is this. He's stayed about three steps ahead of everyone, uses minions that cannot turn against him in any fashion and he can off with a thought if they try, uses his Psychic Link with Dan both to free himself from his alternate universe prison and spy on the heroes, and sends his Co-Dragons in the disguise of humans to infilitrait Bakugan Interspace and cause chaos as a distraction while he goes along with his plans. And that's all before he gets out of his prison. Once he's out, he attacks Gundella to lure the Brawlers there so he can still what he wants from Dan and Drago, managing to steal half of it despite the fact that he loses the fight. And then it turns out that his invasion was merely a distraction so he could cripple Bakugan Interspace, leaving the Brawlers trapped there when they return. He then absorbs his last remainingThe Dragon right in front of Dan, tricking Dan into giving him the chance to absorb the last thing he needs. Justified by the fact he's actually the previous season's Big Bad Emperor Barodius, and has done a really great job at learning from his past mistakes.
The Gremlin organization in New Testament is also a bit smarter in how they deal with Touma: while his Anti-Magic can dispel any supernatural ability, rendering their greatest spells useless, it offers no defense whatsoever against ordinary, mundane threats... like, say, an automatic assault rifle. Against ordinary weapons, Touma is just an ordinary human.
The "Unknown Enemy" of Mobile Suit Gundam AGE are notably more intelligent fighters than normal for GundamMooks. For example, one camped outside a hangar and shot inside the moment they start opening the doors to disable mobile suits before they can launch. And when the Gundam appears and disables one of them, the leader immediately scans its new foe, signals a retreat, and destroys its downed ally so the Federation can't analyze it for data. Then they start bombing the colony from outside, where no military forces are deployed. And in the second episode, when a supply crate with a new weapon is launched to the Gundam, the UE it's fighting immediately tries to shoot the crate down rather than let the Gundam have it.
The winner of "most dangerously savvy villain" award, however, goes to Hades Vandein. When he was outed as a suspicious character that may or may have something to do with The Eclipse Virus he intentionally lets himself be arrested, but not before showing an illusion that involved one of the heroines getting sliced in two. He did this to test the limits of the party sent to arrest him knowing full well they would be acting outside the law if they so much as scratch him. His arrest also serves as protection against the aforementioned Huckebein family, as now they have to go through the TSAB to get to him. When he found himself in a fight against Curren and Veyron, he did not attack first and used a distraction in order to blindside the two before revealing that he has the ability to negate Eclipse powers. He then attacked the non-combatant Huckebein Sonica, and took out Veyron in the process, knowing full well about people who protect their comrades.
Reilan from Haou Airen knew that she would NOT get away with having her love rival Kurumi set up to be gangraped. Why did she pull it anyway? Because she used that as a part of a Thanatos Gambit, which would theoretically give her the last laugh — via getting Kurumi traumatised beyond belief, leaving Hakuron with his hands empty as Kurumi would blame him, and having Reilan herself dead and thus away from other consequncesthat could be even worse. It almost worked, even!
Gungnir, aka the Nehushtan Armor from Senki Zesshou Symphogear - right after appearing she tries to kidnap Hibiki and calls Tsubasa on being Wrong Genre Savvy, for thinking that she is the main character here.
In Mobile Suit Gundam a group of Zeon infantry proved themselves very genre savvy: while they had a Zaku, they knew it was no match for the Gundam, so they used it to lure the Gundam out, rush it on jetbikes and place time bombs on it, causing a collective Oh Crap! in the crew of the White Base and failing only because they had no remote to detonate them before Amuro and the crew managed to disable them. It's notable because not only they outperformed anyone else who had tried to destroy the Gundam, but also because M'Quve would use the very same tactic, albeit on a greater scale and with greater resources, to successfully disable the White Base.
In Mobile Suit Zeta Gundam every single Cyber-Newtype eventually turns on their masters. Even Lalah Sune of the original Gundam (a normal Newtype) ends up being very conflicted about which side she should be on. By the time Mobile Suit Gundam ZZ rolls around, Big Bad Wannabe Glemmy Toto has picked up on the trend. Not only does he have a plan in place to get rid of Cyber-Newtype Elepo Puru when she turns on him, but he also has an army of clones of her ready to go; as each one defects he can bring out the next, ensuring himself a constant supply of psychic super soldiers.
Glemmy's also willing to attack the Combining Mecha while it's trying to combine, and at one point, plays on his own status as a Stalker with a Crush to sucker Roux Louka (the girl he is stalking) into thinking he is willing to Face Death with Dignity, so long as it's at her hands (while she contemplates this, he elbows her and makes his getaway). No two ways around it, the kid is good.
In Fairy Tail, Minerva understands that her ally Sting has lost his previous fight due to the Power of Friendship. So she kidnaps his friend Lector, in order force Sting to fight Fairy Tail to save him, thus using the Power of Friendship against the heroes.
A staple of Yakitate!! Japan is bread causing bizarre reactions that increase in strength depending on the quality of the bread in question, until it starts verging into Reality Warper territory. But nobody ever thinks to use these reactions to their advantage, until Kirisaki comes up with a plan for Yukino to make something for the Yakitate 25 competition that warps reality until St. Pierre and Pantasia's scores are reversed. Where Pantasia was mopping the floor with St. Pierre before, now they're suddenly struggling to stay afloat.
Muteki Kanban Musume: Megumi kicks the container with the ramen Miki is trying to deliver, only to find it empty.
Joker of Smile Pretty Cure! has frequently gotten the drop on the heroes by just waiting in the shadows while they go through their new transformations, attacks, etc. and take out the Monster of the Week, then swooping in and making off with whatever he came for in the last five minutes of the episode.
At the climax of Summer Wars, Love Machine faces down the heroine in a game of hanafuda, the ante being the user accounts it's taken over. After the final game, it's down to two - itself, and the program it needs to direct a satellite to crash. The Genre Savvy part? It made the ante - even if it lost, it could still hold onto the GPS program.
La Seine no Hoshi has many one-shot villains, but the real problem is the recurring Punch Clock Villain commander Zaral: he knows all the tricks in the book and uses them, regularly averting Mook Chivalry (his men attack all together and with their muskets, where other villains play it straight and tend to use melee weapons), checking places where nobody sane would hide in specifically because our protagonists may hide there (and if they say nobody will search them there he'll show up immediately after), and successfully realizing the true identity of the Star of the Seine because he lost her near the convent where the protagonist is studying.
Kitakubu Katsudou Kiroku has an interesting example in Botan. Botan is a high school girl, in a gag anime, but she's aware of the fourth wall. She is nervous that the gag anime format won't last, hopefully making her Wrong Genre Savvy. However, Because she's wrong, she's been training for the event that the gag anime turns into a fighting anime. She's trained so hard, that characters in actual fighting anime would be very hard pressed to beat her. She, a tweenage girl, will regularly, to the point where she takes up most of her series' Moment of Awesome page, preforms feats that would leave the heroes from most anime staring in shock. And when they discuss hypothetically what would happen if the series did turn into a fighting anime, she says with no exaggeration that the Four Great Kings would take only two episodes to defeat. She plans to defeat two of the Great Kings, per episode, should the need arise. Thus, she is literally dangerous, because she is Wrong Genre Savvy.
In one of the manga versions of The Legend of Zelda: A Link to the Past, when Agahnim is defeated in Hyrule Castle and forced to flee, he decides not to take any more unnecessary risks. He knows he doesn't stand a chance against Link's Master Sword, but he also knows that said sword only allows those who are worthy and pure-hearted to wield it. Knowing that Link hates his guts already, Agahnim decides to push him over the edge to make him unworthy of wielding the Master Sword anymore. He kidnaps Link's friend Ganty, transforms her into Trinexx, then siccs her on Link. The young hero defeats Trinexx easily, causing it to turn back into a mortally wounded Ganty. As Agahnim expected, this was the last straw for Link, who gets so pissed off he actually becomes susceptible to the Dark World's magic. What Agahnim didn't plan for, however, is for Zelda to free herself and provide a Cooldown Hug, calming Link down and shielding him again.
In Mobile Suit Gundam 00, Aeolia Schenberg despite being in stasis for two centuries before being killed off for good is revealed to be one. He designed Celestial Being and Veda in such a way that it could account for any unforeseen circumstances in accomplishing his vision. Even getting shot by Alejandro Corner does little more than activate Trans-Am and the true potential of the Gundams.
In Pokémon Special, while the Team Flare grunts may not be necessarily effective, it's clear that the higher-ups are doing whatever they can to make sure that their plans go smoothly. Chasing down the kids who have the McGuffin? Learn everything you can about them as to make better traps for them, and actually try to kill them if possible. Keeping what actually destroyed an entire town secret? Infiltrate the news stations so that masses don't know the truth, and imprison the town's population so that they can't blab either. To further rub salt into the wound, loot all their stuff afterwards for possible valuables, including all their Pokemon.
In Gundam Build Fighters, Sei builds a system into the Build Strike Gundam's shield that absorbs beam attacks and uses the energy to power up the suit in various ways. After it' awesome use in the first round of the World Championship tournament, the next ace fighter he goes up against it shoots it once to confirm its ability, then immediately moves to disable it. Subsequent opponents likewise make eliminating the Build Strike's shield their first priority.
Death Gun from the Phantom Bullet arc of Sword Art Online is incredibly savvy in predicting Kirito's moves because they fought before in SAO. When a player with Kirito's name and sword skills shows up in the Bob tournament, he correctly assumes it's the same person and confronts him face-to-face in order to confirm it. Then, during the finals, he waits until Kirito and Sinon have split up before ambushing Sinon, knowing that in addition to being one of his planned targets, if Kirito was the real deal then he would go on a Roaring Rampage of Revenge in response to Sinon's death. And when Kirito and Death Gun finally battle, Death Gun reveals he's prepared for a sword fight with Kirito by averting Villain Forgot to Level Grind by practicing his Sword Skills to point of muscle memory, and by preparing a weapon similar enough to what he used in SAO, while meanwhile Kirito is stuck using a weapon that's lighter than what he normally uses.