Neo Angelique

A re-imagining of the Romance Game/Dating Sim Angelique series, it debuted as a PlayStation 2 game in 2006. In 2008 it was adapted into a TV series, Neo Angelique: Abyss. It has a total of 26 episodes, over two 13-episode arcs. focusing on a girl named Angelique who is uniquely qualified to battle the Thanatos, ephemeral beings who suck life force out of humans.

Tropes used in Neo Angelique include:

Arcadia
Badass Automaton: Both Jet and J.D.
Badass Bookworm: Rayne
Batmanambit: Nyx's decision to find and befriend The Queen's Egg.
Big Bad: Erebos, who created the rift that allows the Thanatos beings to get into Arcadia.
Blonde, Brunette, Redhead: Hyuuga, Rayne, J.D., and Nyx.
Break the Haughty: Erenfried is initially presented as a insufferable prodigy until his inventions stop working on the thanatos, his team is wiped out in a thanatos attack, his plan to kidnap Angelique fails causing his mentor to scold him, this same mentor gets sentenced to death for the property damage Erenfried's machines caused forcing him to ask for help from The Organisation, he is forced to give up his robot assistant and once he finishes his work The Organisation betrays him and throws him in prison. He's a bit different after all that.
Cast Full of Pretty Boys: One major female character, the rest are hot pieces of cheese.
Censor Steam: Hyuuga in the pond, Roche in the shower, the list goes on...
Cool Shades: Jet's Oakley-style glasses that still allow him to glare.
Deceptively-Human Robots: The Jasper Dolls
Decoy Leader: Mathias as Head of the Order.
Dual Tonfas: J.D.'s weapon of choice.
The Gunslinger: Rayne, who can shoot a coin in the air multiple times and never runs out of ammo.
Hot Scientist: Rayne, oh god, Rayne!
Impossibly Cool Clothes
Lost Technology: Experimenting with this gave Rayne his Purifier powers.
Masaya Onosaka: The seiyuu for J.D.
My Grandson, Myself: Nyx
Non-Human Sidekick: Erwin
Scary Shiny Glasses: Erenfried frequently, and Nyx occasionally.
Schizo-Tech: Horsedrawn carriages alongside cars; 19th Century attire next to modern goth; and so forth.
Shirtless Scene: Several characters get to flex their pecs to an adoring fanbase.
Spell My Name with an "S": J.D./Jade, Rayne/Lien, Erwin/Ervin, etc., mostly due to translation.
Spoiler Opening: The first opening spoils Rayne belonging to the artifact consortium, J.D. being an artifact, Nyx being Erebos and the death of Carlyle. If you had played the game however you would already know these things.
Super-Hero Origin: Rayne's powers were artificially created.
Thirteen Episode Anime: The anime spin off has two seasons that consists of thirteen episodes.
Title-Only Opening: Found in Second Age. Seems to be one of the common tropes for the Neo Romance franchise.
True Companions: As each new Purifier is revealed, Angelique convinces them to join the rest of the team as companions. As the most formal character, Hyuuga has trouble speaking familiarly with other team members.