Nisha the Lawbringer: A sociopathic gunslinger who would eventually become the Sheriff of Lynchwood and Jack's significant other, as well as an optional boss of the "Showdown" mission in the second game. Her Action Skill, titled "Showdown", makes the screen fade to sepia while buffing her stats and automatically locking onto enemies. Her trees include: building "Order" and "Wanted" stacks to boost her damage, stats and health; boosting her guns/Showdown ability and letting her dual-wield pistols; and perks that benefit rifles and hip-firing, up to being able to turn her enemies into bombs.
Bad Boss: Evidence seems to be pointing to Mr. Tassiter, Handsome Jack's boss, as being this. Granted, Handsome Jack is not by any means qualified to call anyone a Bad Boss considering what he puts his employees through in Borderlands 2, but this is before his descent into insanity and evil and it's implied that Mr. Tassiter drove Jack at least partly nuts, so make of that what you will.
Batman Can Breathe in Space: Averted. With the exception of Claptrap, players have to watch their oxygen supply in areas that are devoid of atmosphere. It ticks down at about 1 point per second, and can only be recharged by using Ozkits or running into oxygenated bubbles and areas of the map. Likewise, fire weapons (and possibly some other elementals) only work in oxygenated environments. The bandits need O2 as well, and will go running towards these areas if a fight draws out too long or if you headshot their helmets off.
Body Double: The first DLC character of the game is "The Doppelganger", Handsome Jack's bodyguard who was surgically altered to look just like him.
Combat Sadomasochist: Nisha, and it's reflected in her Law and Order tree, which is focused on getting buffs from giving and receiving damage.
Comically Missing the Point: A teaser has Handsome Jack reciting his own version of Ozymandias with himself in the place of the title character. He's brought up short in confusion by the line "Nothing beside remains," and changes the rest of the poem to a hymn praising his own awesomeness (and handsomeness) because if he'd taken the time to think about the poem's actual theme he wouldn't be Jack.
Ditto Fighter: Fitting considering that he's the series' mascot, Claptrap's special ability allows him to randomly take on a skill, some of which are those used by the Vault Hunters of the previous game.
Drill Sergeant Nasty: The Dahl Reconstruction System talks like this, in contrast to the female voice that the Hyperion New-U system uses.
Jack's Twitter account gives a Hand Wave as to why they aren't in Borderlands 2, despite that game taking place later: the cryo weapons rely on liquid methane, which tends to evaporate outside of Elpis, and the laser guns are too flimsy and crumple in Pandora's atmospheric pressure.
Excited Show Title!: Rather than just "Pre-Sequel", the game's title is given an exclamation mark.
Foregone Conclusion: As a prequel, it is already known what happens to the four player characters and to their boss. Claptrap becomes the Last of His Kind after Jack destroys his product line. Jack goes on to become the president of Hyperion with Wilhelm and Nisha continuing to be his chief minions, and Nisha and Jack start a relationship while Athena at least survives the events of the game. Most importantly, Jack, Wilhelm, and Nisha are all dead by the end of Borderlands 2's campaign. Still, there's a lot of questions...
Framing Device: The game is set up as Athena recounting the events of Elpis to the Crimson Raiders after the events of Borderlands 2. The New Game+ is her retelling the story to Tiny Tina, who tells her to make it "more difficult" while also adding in her own commentary on the story.
Good Bad Bugs: Invoked with Claptrap's VaultHunter.exe skill, which is considered malware in-universe. Due to it being buggy software, it's abilities occasionally apply to other players, whether this be increased fire rate/reload speed, tossing out grenades uncontrollably or even giving everyone floatation devices so that they bounce uncontrollably around the field.
Mr. Torgue: IT'S NOT MALWARE, IT'S A FEATURE.
Gravity Screw: Due to the game taking place on the moon, gravity is lower than usual, allowing for higher jumps and greater air time.
Ground Pound: One of the abilities introduced. Done by crouching in midair, explained in-universe as a function of your jetpack/oxygen tank.
Healing Shiv: One of Athena's upgrades turns her Aspis into this — throwing it at an ally who is in Fight For Your Life mode will revive them.
An Ice Person: A new element introduced to the series is Cryo, which can freeze enemies solid.
Interquel: As the title indicates, the game takes place between the first and second games.
Item Crafting: The Grinder lets you make a gun by feeding it gear that you don't want.
Jet Pack: The players come equipped with oxygen-powered jet packs that let them perform double jumps as well as a ground pound when in air.
Madden Into Misanthropy: Appears to happen to Handsome Jack during the course of this game. Compare his reaction to Colonel Zarpedon shooting a laser at the moon on the grounds that there are "innocent people" there, to... well, almost everything he does in Borderlands 2.
Mission Pack Pre-Sequel: Built on the exact same engine as Borderlands 2, with the same core mechanics, equipment, and gun brands, with the exception of having renamed the Bandit manufacturer to "Scavs". It was also considered to not be full price, a common trait of Mission Pack Sequels, but it starting price point ended up the same as every other Borderlands game. The developers themselves have even described it as a sort of "Super-DLC".
Mook Medic: The Lost Legion has field medics among their soldiers, able to heal others in their vicinity.
Nominal Hero: Jack takes it upon himself to "save" the citizens who live on the moon from an "evil army".
Power Fist: One of Wilhelm's skills gives him one.
Promoted to Playable: Wilhelm, Nisha, Claptrap and Athena went from bosses and quest givers to playable characters. In the case of Nisha, she's even given an actual name whereas in Borderlands 2 she was known only as the Sheriff of Lynchwood.
Space Is Noisy: It seems that being in space does not negate sounds from either your gun or your enemies.
Start of Darkness: The game tells the story of how Handsome Jack went from a well-intentioned code monkey to the megalomaniacal Big Bad of the second game. The same goes for Wilhelm to some extent, showing how he went from a mercenary to the monstrosity that defeated the original Vault Hunters. Subverted in the case of Nisha, who was already cruel before she met Jack.
Suddenly Voiced: Compared to the previous player characters of the series, who only spoke during combat and were finally given interactive dialogue with Tiny Tina's DLC, the playable characters of this game will openly comment on the plot at hand and even have unique interactions with certain NPCs and each other.
Claptrap: I'm programed to be foolishly optimistic in situations such as these.
Token Good Teammate: Athena objects to the morally questionable orders that Jack gives. The developers have said this was an intentional contrast with Wilhelm and Nisha. Then there's Claptrap, who's only helping out because his programming forbids him from doing otherwise and eventually helps out the new Vault Hunters in the second game kill Jack.
Underground Monkey: One of the enemy types are moon drifters — they look like regular drifters, except blue and crater-y.
Villain Episode: The game's playable characters include two villains from the second game with Handsome Jack leading all four player-characters.
Villain Protagonist: At the very least, played straight for Jack, Wilhelm and Nisha. Claptrap and Athena are more ambiguous (especially the latter, who is the only character whose fate is not already known).
Visual Innuendo: Miss Moxxi's side purse shows two planets side by side while a rocket ship blasts off between them. "TAKING YOU DEEP... INTO SPACE."
Weird Moon: The game takes place primarily on Elpis, the moon of Pandora. The floating Hyperion Space Base in orbit acts as the moon to the players (except now it's being seen from the back, unlike in the previous game).