Noble Demon: Spelled out by Holly: "Deep beneath the layers of deviousness you have a spark of decency. Perhaps you could blow on that spark once in a while". Artemis says he might consider that.
Enemy Mine: In the second book, where he teams up with the fairies in order to track down the source of the goblin batteries, and the third book, where he requests their assistance after Butler is shot.
Enfante Terrible: He's 12 in the first book but it's implied that he was like that for years before the start of the book.
Even Bad Men Love Their Mamas: His mother is a Morality Pet in the first book as he genuinely cares for her and takes care of her. He even parts with half his hard earned gold to cure her insanity.
Even Evil Has Standards: Even when a Villain Protagonist, Artemis would not stand for mistreatment of the environment. He also abandons kidnapping schemes at Butler's request after their first tangle with the fairies, when they discover how human they are.
Evil Plan: In the first book, it's extorting gold from fairies to rebuild his father's criminal empire. Starting with the second book, his plans become less evil.
Friendless Background: Butler is more like a father that takes orders than a real friend. There's a real Tear Jerker in The Artemis Fowl Files, where it is revealed that he used to keep sweets in his limo in case he ever made friends.
Geek Physique: The only muscle he cares about is his brain. The rest of him is scrawny.
Gender Blender Name: Artemis is the Ancient Greek goddess of archery, the moon, and hunting (though he claims the name itself is a genderless noun in Greek). There's an awesome moment in EC where Artemis uses this to deliver a code phrase, as he's explaining to Spiro about his name.
Meaningful Name: His last name may be a reference to Guinea Fowl, one of the animals associated with his namesake —the goddess Artemis, and is said to be her favorite animal.
Mismatched Eyes: After he and Holly accidentally trade eyes during the Time Travel sequence in book five.
Nerves of Steel: In The Lost Colony, after Holly was fatally stabbed, he was able to keep himself together enough to maintain the bomb's erratic countdown in his head and figure out the exact moment to act to retroactively prevent her death — all while they were under assault by a horde of demons.
Overlord Jr.: Albeit one whose overlord is missing in Russia.
Pet the Dog: His treatment of the endangered lemur in book six is probably the most prominent example. Also, in book three, his (begrudging) decision to donate Spiro's billion dollar fortune to Amnesty International, with 10% going to the Fowl Estate as a finders fee, and his request for Holly to heal his mother in book one.
Ship Tease: With Holly starting in book 2. He thinks of her as being 'pretty in a dangerous way. Black widow pretty.'
Shoot the Dog: In the Time Paradox, with the lemur. Subverted in that he actually saved it, but didn't remember doing so.
What The Hell, Villain?: At the end of the first book, Butler calls him out on kidnapping the very human-like fairies and using his mother as an unwitting test subject for an experimental escape mechanism from a fairy superweapon.
Wise Beyond Their Years: At thirteen, he'd already done enough to earn an active file from Interpol.
Deuteragonist: Just in the first book, her actions form half the narrative. In fact, one could chop off the first couple chapters and it would look like she was the main character.
Hero Antagonist: In the first book, she's the honest cop doing her job, while Artemis is the criminal mastermind endangering her society for his own greed.
Battle Butler: Not only is he a perfect example, being an armed martial artist and personal attendant, the Butler family is the origin of the word "butler".
Big Brother Instinct: Juilet's safety is his highest priority. It overrides his training and Artemis' orders.
Genius Bruiser: He's huge because of muscles and an expert in anything military (weapons, tactics, etc).
Husky Russkie: In Name Only, mind you. He's technically Eurasian, and is very culturally neutral thanks to his training.
Legacy Of Service: His family's been with the Fowls since the Third Crusade, and every time a new baby is born they're assigned a Butler to care for them. Naturally, the Fowls are rather attached to them.
Midnight Blue Eyes: In the first book, a man looks into them and notes that "they were a deep, dark blue, almost black. There was no mercy in those eyes."
My Master, Right or Wrong: He doesn't really care what Artemis is doing because it's his duty to help him do it.
Real Men Wear Pink: He apparently likes romantic comedies, his favorite film being Some Like It Hot. He reads romantic novels when nobody is around, though he would never admit it.
Younger than They Look: After being bought back to life by Holly Short, he was aged by 15 years, meaning that he was physically 55 at the age of about 40.
"By the time she was fourteen, Juliet was a third-dan blackbelt in seven disciplines, could dissemble and reassemble any weapon blindfolded, and could do her makeup in under four minutes."
Cute Bruiser: A particularly hilarious example is her playing dumb-blonde teenager for Pex and Chips in The Eternity Code and then knocking them both out.
Morality Pet: She's the only one allowed to laugh at Butler and one of two people allowed to called Artemis 'Arty'.
Never a Self-Made Woman: In the first three books, when all she wants to do is live up to the Butler legacy. Unfortunately, between her decision to make her own name coincides with a Retcon and she then runs off to join a lucha libre troupe.
Professional Wrestling: Juliet's a big fan, and she runs off to join a lucha libre troupe after the third book.
And then the sport itself appears in the seventh book when she and Butler fight off an attack during a show.
Put on a Bus: After The Eternity Code, she goes off to become a pro-wrestler.
Reasonable Authority Figure: Understands the need for procedure but also for adapting to the situation. Its stated he won't believe anything without evidence, thus implying he'll give anyone the benefit of the doubt if they have it.
Vitriolic Best Buds: With Mulch apparently. He's testified against him "15 times" and calls him 'convict' but when Mulch fakes his death Root is immediately sad and called him "One of the constants of his life." Mulch for his part calls him by his first name and doesn't much of a grudge for the '15 times' thing.
Mulch Diggums
Big Damn Heroes: To Artemis and Holly in the Eleven Wonders Exhibition in book four.
Big Eater: Party-size sherry trifle, a bottle of Moet champagne, a chicken, a t-bone steak, fruitcake, a Pavlova, a whole rack of lamb in one bite, two baguettes, a coctail of dairy products... and that's just the part of one meal actually described. Then there's the whole issue of super-fast tunneling via eating dirt and expelling it.
Boxed Crook: In the first three books. He joins relatively of his own volition later.
Gasshole: He tunnels by eating dirt and his method of disposal and propulsion is this trope.
Fartillery: He can uses his gas a method of attack. Its descriped as a 'mini-cylcone' and 'dozens of sledgehammers'.
Genius Bruiser: While not on the same level as Artemis (duh), he is quite crafty and good at what he does. Even Artemis can't match him in geology. He is also fully capable of biting anyone's head off... or blowing it off with Fartillery.
Kansas City Shuffle: By refusing to help Root in book 1 he tricks Da Chief into thinking he wants a lighter prison sentence, when in fact he plans to escape outright. Then extends the trick by faking his death and stealing the other half of the ransom gold.
Never Live It Down: In-universe, for selling a Jules Remy trophy to the undercover LEP and later "laying low" in a Los Angeles penthouse whilst "collecting" Academy Awards. A prison warden was highly amused.
Mission Control: He directs RECON missions from his computer room.
The Smart Guy: Taking him out of his computer room is like taking the brain out of RECON.
Ultimate Job Security: He deliberately angers his boss and decorates RECON's equipment however he wants but there are two reasons why he is never fired
As noted above, he's a Bunny-Ears Lawyer: while he may be a little odd he's extremely good at what he does.
Vetinari Job Security: He built the computer system and hid a virus that will crash it if he's not there to boot it up.
Voice with an Internet Connection: Perfectly summed up in this line "I'm right there with you, darling. Unless you trigger a land mine, in which case I'm in the Operation Room." Most of his 'field' time is this: talking through a headset to people in the field and supplying them with info.
Something of a Fridge Brilliance, or maybe just plain Homage. In Greek Mythology, Orion was an excellent hunter and became Artemis' hunting companion. In some variants of the legend, he bested Artemis at hunting.
Let's Get Dangerous: In the book's own words, he "sped up, showing a nimbleness that anyone who knew the boy would not associate with him." And after that,he disarms Turnball, and uses his gun to accurately disable Holly.
White Sheep: He's latest head of a long standing criminal family that wanted to be a legitimate businessman.
Angeline Fowl
Apron Matron: Seems to be becoming one of these in later books.
Demonic Possession: Angeline's "illness" is actually this in book six, by Opal.
Morality Chain: Has a hold on Artemis Sr's (and to a lesser extent Artemis Junior's) Morality Chain.
Proper Lady: Hidden at first but once she recovers she's described as carrying herself with dignity and grace, as well as ordering the house hold, finances etc.
Kick the Dog: Not only did she kill Root, she tricked Holly into speeding up his demise by shooting the bomb wrapped around his waist, claiming there was a weak spot.
The Man Behind the Man: While the B'wa Kell has not always worked for her, she and Cudgeon helped orchestrate it's largest historical campaign against the LEP. She is also this to the Extinctionists in book six.
Tempting Fate: In the fourth book, she arrogantly proclaims that magic is of no use to her, and she will rely on science instead. When she needs to use her mesmer powers on a human at the end of the book, it backfires on her.
Villainous Breakdown: Experiences this after Artemis tricks her into detonating the charges needed to complete her plan on her own shuttle, ensuring that her Evil Plan will fail and leaving enough evidence to show that she was behind everything.
Briar Cudgeon
Ambition Is Evil: His 'favorite daydream' of a Council seat leads him to one questionable act after another, leading to the following tropes.
Combat Pragmatist: On his first arrival at the Fowl Mannor, he wanted to blue rinsed the whole place immediately. Quick, unexpected, clean, and completely against the rules.
Engineered Public Confession: Foaly sends a conversation of him admitting his plans to betray Opal to Artemis' mobile phone near the end of book two.
Fallen Hero: One of the few on a First Name Basis with Root because of their long friendship and the former's respect for his integrity and sense of duty. Then he lets ambition get the best of him.
Lady and Knight: Has this Dynamic Opal Koboi The Artic Incident. Opal is the ojou who does her techo-wizardy from a safe distance and Cudgeon is the Fallen Hero in the thick of things. "I shall be the hero of the resistance and you shall be my princess."
Though there were a hundred guards mentioned at some point and it's heavily implied that the two henchmen are doing one small task out of a big organization.
Anti-Villain: Somewhat. His motivations in The Atlantis Complex are sympathetic, but it's made clear that he has been anything but an Anti-Villain throughout his career. Artemis states at the end that he finds it hard to really see Turnball as a villain.
Better to Die than Be Killed: In LEPrecon (in the Artemis Fowl Files), he swallows a lethal spider rather than let his brother take him back to prison. Julius manages to save him, though.
Shiny New Australia: In light of Opal's narcissism and madness, the only thing keeping them loyal, aside from fear of punishment, is the thought of sipping alcoholic beverages on the beaches of the Carribean after Opal's world conquest.
Dragon with an Agenda: To kill all demons. He ends up betraying Minerva and holding Nš1 hostage because of it.
Freudian Excuse: His brother made up stories about him fighting shapeshifting demons to cover up his nightly gang escapades. When murdered in a gang war, his brother was driven to kill the demons that supposedly took his brothers life.
Chekhov's Gunman, Chekhov's Skill: Almost literally, as it's less the character himself than his psychological skills that end up important in book four, as they help house Opal Koboi.