David Versus Goliath: Bastion-Sigma vs. Zwei Trinity, with the later being a towering behemoth in this situation. Unlike most of the cases of this trope, the Bastion-Sigma was actually trashed, along with its pilot, during their encounter. And then they stood up once again, in order to finish the job before collapsing due to the damage both suffered.
Darkness Equals Death: The first phase of the fight against the Trinity, involved Eins covering the entirety of Echo-City with a thick black nananites' cloud of which rendered nigh-useless most of the mechs' visualization and tracking devices.
Dramatic Irony: Dan and Summer claim they are nothing like Psychic Reaper when (during the Mind Rape) it tells them they are half-Eldritchian. Yet they are in fact half-eldritchian/half-human and have psychic powers.
Dude, Not Funny!: In-universe case. Dan and Summer laughing at Emil punching Faith during her abrupt mental-breakdown was unnecessarily cruel. Emil, Samson and Gerald didn't hesitated to chastise them due to their unappropriated reaction. (with Gerald going one step further and out-right punching Summer in the face)
Dysfunction Junction: Nearly the whole squad has some sort of issue or problem they have to deal with.
Earth Is a Battlefield: Par for the course, with at least half-a-dozen Eldritchian's attacks occurring all around the world every single day.
Eldritch Abomination: The main aliens and the monsters they send to attack Earth. They've even been nicknamed (in and out of universe) as Eldritchians.
S.E.V.E.R (Seeking Eternal Valkyries Enjoying Renounce). The name of the council of SERVE's leaders.
GeneSys stands for for Geo-Experimental Nourishment Enhancement Systems, a name which roughly describes their original purpose... Before they started focusing on creating weapons to fight the Eldritchians.
Genre-Busting: Can be described as a mix of Action / Sci-Fi / Humongous Mecha / Cosmic Horror / Psychological Horror and Drama.
Half-Human Hybrid: SERVE's dubious experiments have involved this. And Dan and Summer are prime examples thanks to their parents' actions. Also, the existence of half-human half-Eldritchian hybrids (also know as Fae) has been confirmed.
Hoist by His Own Petard: The Psychic Reaper tried to break Emil by prying into his guilt by creating an apparition of his dead Captain, but instead; it merely gave the Pilot closure and the willpower to fight the Alien's psychic powers. Same with Hans at it allowed him to find out about Gustav.
Hot-Blooded: Quite a few pilots, just check the Character Page for more information.
Of the "lost" pilots, we have Bethany, who was a seriously twisted case of this trope.
There's some really bad blood going on between SERVE and GeneSys, stemmed in great part due to their drastically different approaches when it comes to dealing with the Eldritchian. The former wants to study them in order to use their powers to help mankind, the later wants to destroy them completely in order to prevent mankind's extinction.
Also, there's a lot of tension between SERVE's different branches and members.
Made of Iron: Most of the Marine Corps' operatives, including George and Jack, can survive injuries that would be fatal or game-breaking for other pilots, and they recover way faster than any of them. As seen during the fight against the Trinity, where both of them stood up and continued fighting even after receiving some substantial injuries.
Mildly Military: SERVE is a direct creation of the UN and they send out multiple planes, tanks and mechs for battle. Justified in that they were created sorely to tackle the Eldritchian threat head on.
Modesty Bedsheet: Celeste used one during her stay at SERVE's medical ward, in order to allow jack to patch the wounds that Leo inflicted on her during her ill-fated attempt to give him a hug. Later on, it lead to rather embarrassing situation involving Dan and a ridiculously muscular male nurse. (who wears sunglasses and a blond pompadour!)
Monstrosity Equals Weakness: Generation-3 Fae appear to be more bestial in behavior and mentality. It's not sure if their powers are inferior to the more humanoid iterations created after them, but they have been deemed nigh worthless by creators, mostly due to being too "unwieldy".
Mutants: Terrestrial animal life-forms which enter in direct contact with Eldritchian's tissue are bound to be transformed in extremely unpredictable ways, while also turning feral in the process. The protist and plant kingdoms, and some simpler organism like the insects and vermin, are immune to these mutations; because, if they weren't, life on Earth would have been completely assimilated in just a couple of months.
Not What It Looks Like: Dan and Celeste were caught in a situation like this during her stay at the medical ward. Turns out that a bare-chested girl giving a hug to socially-awkward teenager while they're both sitting on a bed, can be easily misinterpreted, who would have thought?
Gdolkin (Blue) and Krueger (Red). However, the twist about them is that their mechas' role are reversed; Gdolkin's mech, the Ferrus Manus, it's a close-range mech, (Red) while Krueger's Bjorn, the Fell-Handed, is a gun-slinger mecha. (Blue)
Hans (Red) and Emil (Blue) also have this kind of dynamic, (after forming their Odd Friendship) with Hans over-flowing with (dangerously) unbounded emotions, and Emil being the most level-headed and prudent pilot in the whole Delta squad.
Retirony: Discussed by Celeste, who says that if something terrible happened to her in the next mission after revealing her plans for the future, that would mean “that the universe has an extremely cruel sense of humor ”.
Running Gag: It seems that Gerald has an uncanny (and somewhat alarming) tendency of getting punched or kicked by the Delta Squad pilots. So far, the list includes Hans and Katherina.
Sacrificial Lion: During the fight against the Trinity, the Delta Team suffered its first major casualty: Hans Liddmin, thanks to a combined attack between Eins and Zwei.
Sarcasm Failure: Hans's reactions to Gainax making their lives into an Anime.
Shoot the Dog: A minor, but still significant case. Emil didn't enjoy punching Faith during her breakdown, but he had to do it to prevent her from seriously hurting Summer.
Wave Motion Gun: Dan has one in his mech and it is one of the many mech weapons.
What the Hell, Hero?: Gerald and Faith call out Dan and Summer for killing the just born child of Psychic Reaper, the eldritchian that invaded and attacked the SERVE base mind raping most of the squad. Subverted in that Dan and Summer both thought the baby eldritch was the monster doing the work and as such they were right. The unborn fetus that just got born was the Psychic Reaper and they knew this because of their latent psychic powers.
Almost everyone in SERVE also calls out Faith for standing by and doing nothing while the Psychic Reaper mind raped her teammates. Faith immaturely reasons that she did nothing because the monster was favoring the rest of the team and she decided to watch how they fight. She notes that even when it did try to mind-rape her, her life was so unconventional that it couldn't dig up anything effective. No one was swayed by her explanation regardless.