You're the Big Bad and all your Evil Plans are thwarted. The hero can take anything you can dish out and then some, the Mooks cower in the corner whenever he so much as looks at them, and The Dragon is kindly recommending that you run for the hills. Can nobody stop this unstoppable juggernaut of justice? The answer is no.
Enter the Laser Guided Tykebomb, a henchman with one purpose in life and one purpose only: to take down the good guys. The LGT may be a specially constructed robot, a human raised from birth to carry out the deed or normal minion promoted from the ranks to fill the role. This nemesis will often have powers designed to counter or match its targets, or be equipped to exploit his Kryptonite Factor.
Another scenario has a character feeling a Face-Heel Turn coming on, so they need someone to kill them as a kind of Suicide by Cop, except no "Cop" is strong enough so they have to make their own.
Can often overlap with Hero Killer.
Heroes have been known to be created this way to destroy specific villains, in which case their creators are generally morallydubious.
Subtrope of Tykebomb.
The Mini-Cons are a race of LGT in Transformers Armada, created by Unicron to sow strife and feed his hunger for negative energy.
Tsukihime has a whole family of them, known as Demon Hunters. Notably, they don't hunt demons, because that's a job best left to priests with access to exorcism and other forms of anti-demon magic. They hunt people with any traces of demon or otherwise non-human blood, who by nature of their heritage have demonic magic and powers, and the inevitable risk of one day losing their human traits entirely and going insane. Therefore we get a family of Badass Normals who get Training from Hell since birth and feel an irresistible impulse to brutally kill anything that feels inhuman but looks human (they're also slightly psychic).
To be specific, exorcism rites and binding spells don't work on hybrids, so you have to deal with something that's as strong as a demon, actively violent and can't be slowed by magic or taken down from a distance easily. Also, Arcueid with regards to the fallen True Ancestors. They're True Ancestors who aren't bothering to suppress their blood lust anymore and are therefore too powerful to be killed normally. Well, they were.
In Dragon Ball Z all the androids were made and somehow designed to kill Goku in order to avenge the Red Ribbon army. They choose otherwise, anyway.
Only 17 and 18 choose otherwise. 19 remains faithful to Dr Gero and 16, while he doesn't seem to lament the loss of his creator, still wants to kill Goku. The last one is bizarre when combined with 16's love of life and extremely calm demeanor.
Being purely robotic (17 and 18 are Cyborgs, made by upgrading a pair of human siblings), 16 was initially unable to overcome his core programming. However, he absolutely refused to engage in any violence against anyone or anything other than his designated target until the threat of Cell presented itself. He does meet Goku face-to-face near the end of the saga, but restrains himself from attacking, because that isn't what he wants to do.
In BleachWonderweiss's Resurecciˇn turned out to be specifically designed by Aizen to block Genryūsai's flame zanpakuto's powers.
Schrodinger from Hellsing, who was created for the sole purpose of poisoning Alucard.
Lady Snowblood has a extreme example. The protagonist was concieved in jail solely as a means for her mother to take revenge on those who hurt her and her family. Add a lifetime of Training from Hell and a Parasol of Pain, and cut her loose with a list to hunt every last one down. The protagonist even comments that she is not a person, merely a "phantom of [her] mother."
In Rave Master it's the Big Bad, Lucia who fits the bill. His isolation as a child resulted in him having little contact with sentient creatures other than a fragment of Endless who, despite not having quite enough control over him to be a Man Behind the Man, convinced him that the sole reason he existed was to trigger the world ending 'Overdrive' explosion.
Eren Yeager, the main character from Attack on Titan becomes one as a result of witnessing a Titan devour his mother, swearing to exterminate every last one of them. This is aided by him gaining the ability to transform into a Titan, with it hinted his father injecting him with a mysterious substance is the cause.
Soul Eater has Crona trained by Medusa specifically to become a being capable of killing Kishin Asura. Shinigami's intention in creating Kid can also be seen as a 'heroic' example of this, as he also fully expected his heir to be able to kill Asura.
In Afro Samurai, the bad guys constructed a robot version of Afro able to mimic all of his abilities specifically to kill him; they may have also groomed Jinnosuke for this specific purpose.
The Scorpion and the Spider-Slayer robots in the animated Spider-Man series as well as the comics.
The Marvel Universe has the Sentinels, a series of robots built for the sole purpose of hunting mutants.
An earlier version of the Sentinels (retconned into existence) is TESS-One, a robot constructed during World War II for taking down Captain America if he ever went rogue.
Marvel also has Drax the Destroyer, created for the sole purpose of killing Thanos. He succeeds. Thanos doesn't seem to mind.
Transmetropolitan had the hero being followed by a young kid with no head. The hero (and the future) is so off the wall nobody is too surprised by the lack of head. The hero throws the kid out a window, wherein he explodes. Turns out it was literally a laser guided tyke bomb, created by one of his many, many enemies.
A very unusual kind of LGT was used in Jabba the Hutt: The Art of the Deal. The first issue had the Hutt travel to a meeting with another crime lord, Gaar Suppoon, to trade valuable resources. After a small ceremony in honor of Jabba, the negotiations started off with Suppoon insulting the Hutt for deigning to threaten him with a bomb. Just in case the threat had been real, he had the Empire send one of their best explosives experts, Kosh Kurp, to search the place, and he turned up nothing. The bartering then began in earnest, with each gangster double-crossing and cheating the other, until Suppoon, having been outmaneuvered by Jabba, lost his temper and attempted to have the Hutt killed. Jabba warned him that if he did not regain his temper, he would detonate his bomb. Suppoon, unimpressed, told Jabba to do so, at which point the Hutt called him "Sonopo Bomoor". After a beat, Kosh Kurp turned to Suppoon and asked if he really was the Sonopo Bomoor, the one who razed the city of Bonaka Nueno on Intuci, and encouraged his blood crazed minions to slaughter Kurp's familyas he, a mere child, watched. The whole situation does not end well for Suppoon.
In The Boys, Black Noir, a Homelander clone who is slightly more powerful thanks to refined Super Serum, was created specifically to kill Homelander if he went rogue. Problems arose when Homelander didn't go rogue. Black Noir wanted to fulfill his purpose so he gaslit Homelander by committing atrocities in Homelander's costume (like raping Butcher's wife) and sending the photos to Homelander, hoping to drive him insane. It worked.
The title character of Hanna fits the trope to a tee.
In The Lion King 2, Zira raised Kovu to be this. It didn't exactly work out for her.
Arguably, the Skywalker twins were set up as a pair of these to take down The Empire and the pair of Sith in charge, with Obi-Wan and Yoda using a combination of Jedi Truth and BatmanGambits to set Luke against his father, even dismissing the notion of trying to redeem Vader / Anakin.
The novelization of Revenge of the Sith defies this trope. Obi-Wan and Yoda ultimately decide not to train the two to fight the Sith (seeing how their training failed against the Sith's conspiracy) and left the twins' fate to the will of the Force.
Hit Girl of Kick-Ass has been trained by her (also badass) father to take down mob boss Frank D'Amico.
The Spartan-IIIs in the HaloExpanded Universe, gathered from children orphaned by Covenant attacks, trained for en masse attempts at destroying Covenant facilities. They were sent on suicide missions, and were created to "trade lives for time." The first chapter of Ghosts of Onyx shows the aftermath of one of these assaults, which leaves only two survivors. In all honesty, the man who proposed the idea clearly was not a "nice" man, while the Spartan-III commanding officer recognises the most definitely horrible necessity of his task and wishes that he had no need for this Dirty Business.
The protagonist Spartan-IIs like the Chief count too, as they were originally kidnapped and created to crush colonial rebellions through assasination. The fact they proved useful in fighting genocidal aliens is merely a lucky accident. It's hard to notice, given the setting, but the UNSC as a whole is far from nice.
In Harry Potter this is inverted. Voldemort attacked Baby!Harry and Harry grew up to be the most effective weapon against him because he unwittingly placed a piece of his soul in Harry when he inadvenerently killed himself when the spell rebounded.
The strategists from Ender's Game were trained to take down the formics — Ender was the unlucky one who was the best at it.
In The Princess 99 the Well-Intentioned Extremist group Birds of Prey purposely send their assasin to Edgewood Academy in order to kill Princess Aurore, a.k.a. Prof. Colette, who is currently teaching there, in the most public manner possible
In Darth Plagueis, the midichlorians of the galaxy created Anakin Skywalker to bring about the downfall of Darth Plagueis and Darth Sidious to punish them for the unethical experiments they performed on the midichlorians.
But the player is technically a laser-guided tykebomb against the Big Bad's rival for power.
The Novus from Universe at War: Earth Assault are an entire species of robots made for the purpose of destroying the Hierarchy, the alien conglomerate that destroyed their creators.
Famously, in Star Ocean: Till the End of Time, Fayt, Maria and Sophia are specifically genetically engineered by their own parents to be able to enter 4D Space and be able to combat anything that they find there.
Tidus in Final Fantasy X is the Laser-Guided Tykebomb against the Big Bad Sin. Of course, you can blame The Fayth for that one...apparently good guys can create a LGT.
Starkiller from The Force Unleashed is a sort of subversion. He was raised like a Laser Guided Tykebomb against the Emperor, but was really raised with the purpose of being bait against anyone who might try and start a rebellion.
Kirah in the penultimate level of Gitaroo Man, our hero didn't see that comming.
In Dust: An Elysian Tail, it's eventually revealed that Dust himself is one of these, specifically created and groomed to stop General Gaius and his army.
Kratos from God of War can be considered one since he was meant to destroy Olympus. He was raised in the warrior culture of Sparta. He was spared by the war gods of Olympus for use in the future. Eventually, his "training" was taken over first by Ares. After they had a falling out over the incident with Kratos' family Athena took over his training and targeted him toward Ares. Ironically, other events set him back on course to destroying Olympus which may or may not have also been in Athena's plans.
Shade Tail / Grace from El Goonish Shive. A rare case of LGT targetting the Big Bad, though the creators of this genetical custom build were far from innocent themselves.
Doomsday in Justice League Unlimited was designed for the sole purpose of killing Superman. This is likely a subtle Mythology Gag to the fact that Doomsday was written into the DCU for the sole purpose of making a "Superman's Death!" storyline.
The Young Justice cartoon incarnation of Superboy. He was created by Project Cadmus (under the orders of the Light) to either replace a missing Superman or take out a rogue one. The villains' tendency to call him "the weapon" suggests they were leaning towards the latter.
The Teenage Mutant Ninja Turtles (2012) version of Karai. Shredder kidnapped her as an infant, raised her as his daughter and kunoichi minion, and had her believe that Splinter killed her mother. As such, she wants Splinter dead. Except Splinter is her father, and Shredder killed her mother...