Arachnid

Arachnid is a manga by author Murata Shinya and artist Ifuji Shinsen. It follows the exploits of middle schooler Alice Fujii as she's briefly and intensely trained by the assassin who killed her uncle, and then has to face off against pretty much every other assassin that the organization can throw at her.

Note that if you have a phobia of any insect at all, you're probably going to have a bad time trying to read this manga. The story regularly stops for detailed drawings of insects carrying out some unique biological quirk, in an attempt to compare it to a human assassin's technique.

Tropes used in Arachnid include:

Absurdly Powerful Student Council: Well, when it's run by the leader of the absurdly powerful criminal syndicate, this makes sense.
Author Appeal: Bugs. Bugs bugs bugs. Murata Shinya loves bugs. It could probably be brushed off as just the theme of the manga, except that at one point the the story stops for a page or so to explain that every single assassin in The Organization uses an insect theme, and that no one makes them do this or encourages them to do it, but that insects are just that awesome so they all do it.
Badass Normal: All the assassins are supposedly this, being merely humans who have trained themselves in insect-based techniques. In practice they've actually got insect-based superpowers.
Blatant Lies: A teacher demands to know what Kabutomoshi's massive spearlike weapon is. She tries to claim it's a mop.
Disability Superpower: Alice has a hereditary brain disorder that is essentially the opposite of ADD... she becomes too focused on things at random. It's supposedly why she does so badly in school and doesn't have any friends... but is never actually shown to be anything more than an inconvenience to her in day-to-day life, and allows her to become the greatest assassin in the world in two weeks after Kumo teaches her some (unexplained) "trick" for dealing with it.
Happiness in Slavery: Gokiburi to Alice. Especially considering the slavery is pretty much at her own insistence.
Insistent Terminology: Everyone except Gokiburi always calls her "Fujii Alice". Always, any time they refer to her. "I've brought Fujii Alice." "Hello, Fujii Alice. How are you, Fujii Alice?" (Gokiburi just calls her "Alice-sama".)
Obviously Evil: The student council president/Boss of the Organization. If the long white hair and elaborate eyepatch weren't enough to tip you off, she walks around with a Slasher Smile that she doesn't bother to hide from Muggles. They don't seem to notice and consider her beautiful and elegant.
The Worf Effect: Gokiburi suffers this. A lot. Originally introduced as one of the Organization's most formidable assassins, Alice quickly defeats her with her usual hax-mode abilities, much like she does everyone else. But then Gokiburi quickly becomes someone any new assassin beats the crap out of to show how tough and evil they are.
Wrathful Wasps: As befitting of a manga that revolves around insect-based fighting techniques, Arachnid has Hornet, an assassin codenamed after the terrifying Asian Giant Hornet. And much like the bug that inspired his name, his fighting style revolves around using analyptic shock-inducing stings to kill his targets.