Ace Custom: The Concept Model trait for the Evangelions. It starts with two free upgrades but costs two collateral damage when it enters battle because of the cost of replacement parts.
Adaptation Expansion and Alternate Continuity — Game Masters are encouraged to expand on the story and mythos as they please (and to throw a curveball at those who have seen the anime).
It also includes elements from the various Evangelion video games, namely the Jet Alone Prime and T-RIDEN-T Land Cruiser.
And I Must Scream - This can occasionally happen to pilots. If your Eva is defeated, there's a chance that your entry plug will fail to eject, leaving you stranded in the middle of a battlefield... and you can probably still feel whatever it was that incapacitated your mech.
Artifact Title - The name "Adeptus Evangelion" referred to the fact that the game used the same system as Dark Heresy. The dev team has announced they will be abandoning this system when releasing v3 (though they are simultaneously releasing a 2.5 version that will use the DH system), but are keeping the title because it is recognizable.
Attack Its Weak Point - As in TheSeries attacking an Angels core with a critical can cause it to explode and cause masses of collateral.
Barrier Warrior - Played with, AT Tacticians can be used to buff and shield allies but they also get some cataclysmic powers.
BFG - Any ranged weapon you wield would fall under this, really; after all, the players characters are piloting 40-meter-tall mechs, so any gun you have would likely be as big as a person, or bigger.
Several guns are so big that even an Evangelion needs the Heavy Chassis upgrade to so much as pick it up.
The Great Positron Cannon is so huge that you can't even fire it if you aren't plugged into the city's power grid... three times. It's also powerful enough to shoot into orbit.
Also played with, Pallet Guns are woefully ineffectual since they just fire Battleship shells that are easily deflected.
BFS - If you get enough Weapon Upgrades you can get a Progression Sword.
Not forgetting the Heavy Lances!
Body Horror - [REDACTED] has a scenario involving an old Evangelion research facility. At the very end of it is a graveyard full of Evangelion corpses, just like in the series... except that these ones will pull everyone stepping into the pit below the surface and (somehow) replace entire limbs with their own! In a rare subversion of the trope, the victim can actually profit from this, if the GM chooses so.
Boss Game - Barring some rare exceptions, most fight tend to only include a single, powerful and unique enemy, making this a rare RPG example of this trope.
Eye Scream - A variation of this can happen if an Eva takes critical damage to its head; the pilot will feel the damage too, which can cause anything from disrupted focus due to intense pain, to going slowly insane from the feeling of your head melting.
Flawed Prototype - Evangelion with the "Patchwork" Drawback, described as being made from recycled pieces, dummy bodies, and duct tape.
Frickin' Laser Beams - The positron rifles came back. And they have three upgrades. One that has a multi shot fuse. One that is a one-shot and is larger. Then there is the Great Positron Cannon. It is able to one-shot angel if you get lucky. Problem is you can only mount it on a heavy chassis. So you become a Mighty Glacier.
Actually, the description of the Great Positron Cannon, alongside the stats, imply that that is the positron rifle used against the fifth and fifteenth Angels in the show. The range and extremely unwieldy nature of it back this up.
Gainax Ending - Not one, but NINE of them are detailed (including the one from End Of Evangelion), each one as apocalyptic as the next.
Godzilla Threshold - Lose a battle, and you cross this, with the UN deploying a N2 mine. Later Operations Directors can call this in, but you'll probly still need to cross it before they will.
Hidden Supplies - Your city will supply you with these. Guns, ammunition, and spare umbilical power cables can be sent to the surface for the Evangelions to use.
Humongous Mecha - Well, duh. In addition to the Evangelions themselves, there's also Jet Alone, the Jet Alone Prime, and the T-RIDEN-T Land Cruiser, in Prototype, Interceptor and Artillery flavor. There's even rules to pilot a T-RIDEN-T instead of an Eva, which has its benefits (no Synch Ratio difficulties, unlimited amount of Structural and Weapon Upgrades) and its costs (only the Skirmisher and Pointman careers are open to you, no AT or Biological powers, limited selection of melee weapons).
Hilarity Ensues - In the new GM supplement you can have the players hold a dance competition starring the Evangelions, have a sports match with the Evangelions, or have the pilots create a 30 second commercial for a sponsor.
The dance competition one has actually happened in at least one campaign that doesn't use the supplement. Said game also had a pop idol pilot's EVA backup dancing for her.
It Runs on Nonsensoleum - The scientists haven't really figured out what an A.T. field actually is.
Ludicrous Gibs - In the manual, there are 8 consecutive pages of critical hit tables and nothing else. Then there is one page with a short paragraph about how angels respond differently to critical damage than Evangelions (since Angels lack pilots), and then there are 8 more pages of critical hit tables. Some of the entries are things like "your Evangelion's head explodes so violently it becomes shrapnel and damages anyone else nearby."
Mecha Expansion Pack - In addition to the standard B-Type armour you can also equip your Evangelion with A-Type (Aerial combat), C-Type (Deep sea combat), D-Type (Magma combat, like the one Asuka used against Sandalphon) and E-Type (Outer Space combat).
Mind Rape - the "Touched by an Angel" scenario of [REDACTED] allows you to RP this. Characters that go through it receive the Cold Blooded talent, giving them heightened resistance against further sanity loss (not counting the amount they lost during the ordeal itself, that is). The exact effectiveness of the talent is determined by how much the victim's psychological issues bother them.
Mundane Utility - Using the Evas for a Dance Competition, or for sports. Supposedly it's to get more data on Synch Ratios but really?
Negative Space Wedgie - the "Horror" part of the [REDACTED] supplement includes two REALLY nasty scenarios involving these.
Nerf - many things were nerfed and buffed in version 2.5. Skirmishers are less of a Game Breaker, AT Powers aren't as expensive, making the AT Tatician less useless, and the Story Breaker Power Dirac Breach was severely nerfed.
No Endor Holocaust - Averted. There's a whole system of subsidiary damage called "Collateral Damage", and it reflects just how badly the surrounding terrain is screwed up after the fighting is over — the higher it is, the less system upgrade points you get as a result, as your organization spends more and more of its budget on fixing the damage. Taken to its extreme with Jet Alone; its Nuclear Powered trait means that if it takes critical damage to the body, there's a 50% chance (5 or less on a D10) that it'll melt down. It does no physical damage, and it stops Jet Alone but the players inflict 100 Collateral Damage on the battlefield. Jet Alone Prime, meanwhile, goes off almost exactly like an N2 Mine, thanks to having an N2 Reactor.
One-Hit KO - Averted using the Fate Point system. In any situation where the pilot would die, they can permanently sacrifice one of their fate points for a miraculous survival. Angels can do this too, so you can't win with a single lucky shot.
Schrödinger's Gun - A favorite of the Operations Directors; some of their talents specifically rely on the other people not asking what they have been up to. One of them allows them to show up in person to save one of the other PCs as long as they haven't done anything location-specific in the last 10 minutes; another allows them to modify one of the city's buildings into a rocket-turret structure, and neglect to mention which building until he decides to use it, at which point it is retroactively decided that he had picked that building ahead of time.
Spell My Name with an S: The A.T. Fields are termed "Absolute Territory" fields in the handbook, as opposed to the opening of the show which hints they should be called "Absolute Terror" fields. The justification the book gives is that Angels use the A.T. field to define what space they can influence the laws of physics in, while humans use a much weaker A.T. field to define the body they house their soul in.
Skirmisher Pilots trained to fight with virtually any conventional weapon, ranging from Pistols to Sniper Rifle to heavyweapons, all the way to meleeweapons but with limited AT Powers.
Impact Survivor: They remember Second Impact and have seen the world at its worst and survived. The resourcefulness and luck that got them through then is still on their side now.
Operations Director: Not a pilot, but the support class, in control of the tanks and VTOLs and Turrets during a battle. However, their key abilities are about giving crucial advise, targetingdata, and coordination.
AT Tactician : The only career without a representative of the show. Pilot with limited weapon skills, but knows the most AT powers. Able to pull off wildly varying things from simple push and pull, floating, to advanced spread patterns like Accelerated Territory, slicing with a wave of their hand, to shooting blasts of force and eventually bolts of what is best described as Anti-soul but are better off using their powers to counteract an Angel's own powers or assisting the efforts of their team-mates and not neutralizing. ATTs should Never Neutralize. They have better things to be doing.
The Beautiful Game: The GM Supplement [REDACTED] includes rules for Evangelion scale Soccer / Football matches.
There Are No Therapists: AVERTED! However they can only help you so much. Made more useful in 2.5, where now you can either reduce insanity by 3 points/month or drop it down to the nearest multiple of 10 (from 68 to 60, 99 to 90, so on). So now Insanity is less of a one-way street, but it takes a while to recover.
There Is No Kill Like Overkill: Referenced by the Borderline Edition in their description of the Linear Rail Accelerator Cannon:
When new, experimental technology proves to be wildly successful as a weapon, the most natural progression is to then build the biggest gun one can possibly make out of it. The simply named "Linear Rail Accelerator Cannon" is just that; a heavy weapons platform borne out of mankind's instinctive desire to push the limits of practicality in the name of overkill.
Too Awesome to Use: Anything that needs you to burn fate points. You are permanently deprived of a fate point that could have saved you from death later on, and it's hard to earn new ones.
What the Hell, Hero? - The [REDACTED] supplement includes options to have a pilot stand trial for crimes against humanity. The crime in question can be anything from accidentally knocking down a building to the completely uncalled-for detonation of an N2 mine or deployment of an Anti-AT field in a capital city. Consequences range from a landslide victory for the defense to execution of the accused with everyone else being thrown into prison as well for not stopping him/her.