Aesop Amnesia: Luna experiences some of this, explicitly, right after being purged of the Nightmare at the end. Specifically, she loses a lot of her self-confidence, won in her successful fight from within against the Night Shadow. Justified, as the combination of the drain to her form from the battle and the damage done to her by the Rainbow of Harmony severely weakens her and causes her to lose some of her memories, especially her memories from the time when she was possessed by the Night Shadow.
And Pony Grew Proud: Specifically, the Ponies of the Age of Wonders attempted to power a global Wish spell with massive fusion reactors. The backlash when the spell failed devastated the world and destroyed its advanced technological civilization, in the Cataclysm. Actually, the spell worked, and nearly destroyed the universe by crashing cause-and-effect — the ultra-powerful Cosmics intervened and eliminated that whole 'timeline' to salvage as much as possible, then caused the Cataclysm to create a new timeline where the Great Wish was never cast.
Androcles Lion: As in the original show with Fluttershy and the Manticore, but taken Up to Eleven in that Luna is manipulating the manticore by direct neural linkage through her "thorn" form, and Fluttershy's mind control powers block, counter and then completely overwhelm Luna's control. After this, Luna frequently refers to Fluttershy as the "mind-witch" — and with respect — when thinking about her.
Bittersweet Ending: As we know from "The Elements of Harmony", Princess Luna is free of the Nightmare. And she's at last found the new incarnation of her One True Love Dusk Skyshine. Only this time he's a mare, Twilight Sparkle. And this isn't an Everyone Is Bi fanon. Luna's clearly hoping that they can wind up togetherdespite this obstacle , but there's no guarantee that this will work for either of them. On a far larger scale, the Nightshadows are massing on the Moon, obviously preparing to launch a major attack against the Earth, and the damage done to her by the Rainbow of Harmony has robbed her of much of her memories of her time possessed, so there's no guarantee that anyone will survive long enough for hearts, flowers and foals.
Black and White Morality: Mostly. The Shadows are pretty much pure evil, and both Princess Luna and the Mane Six are almost entirely good.
The Chess Mistress: Princess Luna is a brilliant tactician and — once she's fighting a battle she can wholeheartedly believe in — completely outwits her possessing Nightshadow.
Clock Roaches: The Cosmic Concepts combined forces to eradicate The World That Was Lost because it threatened to crash the continuum with its acausal paradoxes. Cosmic Luna and the G3 Pinkie Pie directly dueled as part of the resultant battle; Luna barely won.
Code of Honour: One of the things that her Nightshadow fails to grasp about Princess Luna is that she is highly honorable, which helps her resist the worst acts to which it attempts to drive her.
Demonic Possession: What the Night Shadows do to any pony who opens himself or herself to them. The composite entity is then referred to as a Nightmare or Nightstallion, depending on the sex of its pony form.
Where are your friends now? the Shadow hissed, mocking her. Even I do not need you any more — you are now more trouble than you are worth. You will die, here and now, alone in the dark, and I alone will inhabit this vessel. I will kill your friends, murder your species, destroy your world!
The Night Shadows, referred to as "anti-life" and strongly implied to have come from another Universe.
The true Cosmic forms of both the Alicorns and the Dragonequii, which respectively resemble vaguely equinoid Biblical Angels (or King Ghidorah) in the case of the Alicorns, or Lovecraftian Outer Gods in the case of the Dragonequii.
Everyone Is Bi: Averted. Luna still deeply loves her ex-husband Dusk Skyshine in his new incarnation as Twilight Sparkle, but she fears that this cannot be carnal, as Luna is straight and probably so is Twilight.
Evil Cannot Comprehend Good: The possessing Nightshadow cannot grasp Princess Luna's motivations, and even in the final battle calls her abiding love for Dusk Skyshine/Twilight Sparkle a "misdirected reproductive urge." Princess Luna actually lampshades this by pointing this out directly to her possessing Night Shadow as part of a ploy in their battle.
The Exile: The first chapter depicts Nightmare Moon on the Moon, watching the Earth for a thousand years and alternating between madness and relative sanity.
Fighting from the Inside: What Princess Luna does subconsciously through most of the story, and does consciously after she realizes that the Night Shadow is possessing her.
Foalhood Friend Romance: Happens between Moondreamer Finemare and Dusk Skyshine. They meet when Moondreamer and her sister Sundreamer are sent to a school and they wind up taking Dusk's part against bullies. When Moondreamer and Dusk reach adolescence, they fall in love, strongly enough that Luna still remembers Dusk as her great love four thousand years later, and uses this to break free of the Nightshadow's control.
Genius Bruiser: Princess Luna. She is not only a powerful Alicorn, but also a brilliant strategist and tactician, which the Nightshadow hopes to use against Equestria, but which Luna herself winds up using against the Nightshadow in her Fight From The Inside.
The Mane Six in general, especially Applejack, Rainbow Dash, and Rarity.
Also Princess Luna, when she breaks free of the Nightshadow's control.
Heel Realization: Almost happens early in the story, when Nightmare Moon's appearance utterly terrifies Apple Blossom, Sweetie Belle and Scootaloo (not yet the Cutie Mark Crusaders). Princess Luna is a Friend to All Children, so this really bothers her — unfortunately, the Night Shadow clamps down hard on the train of thought that would lead Luna to realize that she is behaving like a monster.
Heroic Resolve: Luna is able to break the Nightshadow's hold over her soul (but not yet body) when she realizes that Twilight Sparkle is her One True Love Dusk Skyshine and the Nightmare is about to kill Twilight.
I Die Free: Said word-for-word by the spirit of Princess Luna to her possessing Nightshadow after the Nightshadow points out to Luna that if the Rainbow kills them both, this Aspect of Cosmic Luna will be rejected rather than incorporated into her Oversoul, due to contamination by Nightshadow. Princess Luna would rather die for real than remain a slave to the enemy of everything she loves.
Intangibility: Two examples in-story, which may actually be related.
Seems to be the natural state of the Night Shadows.
Nightmare Moon can turn herself into "cold plasma" and in this form move undetected and seep into tiny crevices. It's not known if Luna can do this in her normal Alicorn Avatar form, or if this is an Alicorn ability in general.
Longing Look: Luna gives Twilight Sparkle one at the party after she's been forgiven by her sister, then stops when she realizes that if she keeps this up everybody will know her feelings. Bonus points because her expression is actually in the original episode, though probably not meant to be taken that way!
In Fluttershy Is Free, we learn that Rainbow Dash noticed that look, though she didn't figure out the reason for it. If Rainbow Dash noticed something emotional, there's a good chance that someone else did, too. Poor Luna.
Literal Cliffhanger: Nightmare Moon undercuts a cliff ledge, causing Twilight, Applejack, Pinkie and Rarity to tumble down the slope. Rainbow and Fluttershy swoop to save Pinkie and Rarity, leaving Applejack and Twilight still in peril. Applejack manages to grab a protruding root, and Twilight to slow her fall enough that she's able to grab on to the edge of the steeper cliff below and hang on, enacting this trope.
As someone who has been a top aerospace engineer and a Cosmic Principle in past lives, Princess Luna is very much aware of the scientific underpinnings of the Universe, and it shows. For instance, she engages in the controlled ionization of the air to summon thunder, and is well aware that her Super Senses are working on phased graviton emission and reception.
There was no dodging. It was too rapid, too omnipresent. She was overthrown by its sheer mass, she felt its vile smell, its evil presence surrounding her on all sides. She was rolled over within it, ended up on her back, with the Shadow covering every part of her. To her extreme revulsion, it began pressing in against every orifice — that she knew that her spirit body was imaginary did not lessen the foulness of this, for she knew that if it could insinuate itself back into her she would suffer a fate far worse than any mere physical violation. She put all her might into her own shielding, keeping the Shadow from entering her and corrupting her soul. But she knew that she could not hold out like this for very long ...
Applejack, who voluntarily slides down a slope to a dangerous cliff edge to save Twilight from a fall, and later rodeo-rides a manticore — when bucked, she sails through the air grinning in exhiliration, hands-off to Rainbow Dash, and then executes a perfect four-point landing. She wins Luna's admiration for this — when Luna is still being Nightmare Moon!!!
Rainbow Dash, who tries to attack Nightmare Moon at her first appearance, and later raises a tornado around the manticore. When she gets hit by its tail, in a manner which might easily have proven fatal had the stinger connected instead of the tail itself, she goes flying, is dazed, and a few moments later joins a mass charge against the beast. Luna later realizes just of whom Dashie is a Reincarnation largely based on her attitude.
Twilight Sparkle herself, who coolly calculates her way through the whole final confrontation with Nightmare Moon. This not only keeps her alive in the mutual charge (when she teleports) but actually leads Luna to recognize that Twilight is DuskSkyshine, triggering the release of Luna's own soul from the Nightmare's spell and beginning Luna's fight from within against the Night Shadow!.
Luna, to the point that she is willing to wind up Deader than Dead (her current incarnation deleted rather than copied into her Cosmic Oversoul) if it means that she can defeat the Nightshadow and at least die free of its evil control. Luna explicitly invokes this trope, when the Nightshadow warns her that Luna will die for real if she does this:
"You thought I didn't know that?" Luna laughed. "Cowardly shade, I've led Ponies into battle more times then you've tortured kittens. Thousands of Ponies have died under my command, every one of them fearing the same prospect, yet not letting it stop them from doing their duty. Do you imagine me any less loyal?"
Omnicidal Maniacs: The ultimate purpose of the Shadows is to consume all life in our Universe.
Pinkie Pie instantly recognizes Nightmare Moon as an Aspect of Cosmic Luna, which is why she screams even before Nightmare Moon materializes in the Ponyville Town Hall. The last time she saw any Aspect of Luna before that, Luna was killing her and destroying her world, so Pinkie's fear is fully understandable.
Luna has access to all her past life memories, especially those of Moondreamer, which becomes important because it lets her recognize Twilight Sparkle as her reincarnated husband and Rainbow Dash as a reincarnation of one of her best friends. This renders her unwilling to kill Rainbow Dash and makes Luna determined to fight the Shadow rather than let it kill Twilight Sparkle.
As in the original story, the friendship of the Mane Six enables them to attune and synchronize their Elements, producing the Rainbow of Harmony.
Princess Luna's discovery that Rainbow Dash is the reincarnation of her old friend Dash Firehooves provide the initial impetus for her to begin to break the domination of the Shadow over her own soul, in part because the Shadow insists that she try to kill Rainbow Dash, and Luna absolutely refuses to do this.
The Power of Love: Since intense love actually hurts the Night Shadows, this is highly relevant to the story. Princess Luna gains the strength to break free of the mental domiantion of her possessor when she recognizes that Twilight is the reincarnation of her ex-husband Dusk Skyshine, and is filled with this emotion.
Powers via Possession: The reason why somepony would summon a Night Shadow in the first place. Princess Luna became stronger than her sister by doing this, at the cost of her free will.
Precursors: During her exile, Nightmare Moon discovers that the Moon contains many ruins and other artifacts left by pre-Equestrian and even pre-Pony civilizations. This is a throwaway, save for Dusk's old landing site, which is very emotionally significant to her.
Reality Warper: Pinkie Pie, to a slightly greater extent than in canon.
Luna: "After more than a thousand years ... you still don't understand me — or Ponies — at all, do you? If I had room in my heart to pity you, I would. No love, no friendship — nothing but eternal selfishness. Eternal greed, a hunger for the life you do not and cannot ever understand."
Reincarnation: An important concept in-story: at least four characters knew each other in earlier lives.
Pinkie Pie was formerly G3 Pinkie Pie, and is one of the last survivors of the World That Was Not, from which she derives her Reality Warper powers. Cosmic Luna helped destroy her whole timeline. It is unclear to what degree she remembers her old identity.
Reincarnation Romance: Teased, as Princess Luna still deeply loves her ex-husband Dusk but is uncertain if they can be sexually attracted to each other, since after all they are now both mares. Unfortunately for them, this isn't an Everyone Is Bi fanon. Twilight Sparkle remains completely unaware of this throughout the tale.
Shapeshifting: One of Nightmare Moon's powers. The sequel All the Way Back confirms that all Alicorns can at least theoretically do this, but that Luna is particularly good at it.
Ship Tease: Luna is never able to so much as tell Twilight Sparklewhoshe used to be to her in a past life. Then again, they're both straight females. There's enough Unresolved Sexual Tension coming off the Moon Princess to fuel a whole armada of ships, though!
Rarity Belle, as in the original episode, befriends the river serpent. Luna, watching this, is envious of Rarity's charm.
Princess Celestia leads Twilight to ask for permission to stay with her new friends, which is exactly what Celestia wanted her to do. Luna, who has known her sister for a very long time, thinks the following (addressing Twilight in her mind with the name of her earlier incarnation):
Luna: She's going to manipulate you. Might as well let her do it, Dusk. Her games generally turn out well, at least for ponies she likes. Anyway, she's hard to resist. Trust me on this one.
Sugar Apocalypse: The destruction of The World That Was Not timeline by the Cosmics, remembered well by Luna and dimly by Pinkie Pie, who fought each other there.
Sugar Bowl: The World That Was Not, the timeline from which Pinkie Pie originated.
Super Senses: Cosmics who take Immortal Incarnations all get these, tailored to their specialty. Princess Luna has both active and passive gravity detection: she can emit a graviton pulse and see by the return.
Take My Hoof: When Twilight is in her Literal Cliff Hanger, Applejack risks her life by letting go of the protruding root and sliding to the edge of the cliff. Being an Action Mare, Applejack times it perfectly and leans over to grab on to Twilight's forefeet — with her own Earth Pony sucker pad / telekinetic grip. Which isn't strong enough to pull Twilight up over the edge to safety. Uh-oh.
Teleportation: Another Alicorn ability, and also one possessed by Twilight Sparkle even before she becamse an Alicorn. Celestia and Luna are both especially good at this, and Twilight manages to accomplish it at least once in battle.
"What?!!" it howled, twisting, turning to defend its [conceptual] spine from what would have been a shattering blow. "No! You cannot have ... "
Time Abyss: Princess Luna is over 2500 years old in her current incarnation, and almost as old as the entire Universe in her Oversoul as the Cosmic Concept of Gravity.
Two-Mare Industrial Revolution: What Celestia and Luna have been trying to accomplish since they started to unify Equestria, and what Celestia has to largely do on her own after Luna's rebellion — namely, bring about a new Age of Wonders — hopefully one that won't end in Cataclysm this time round.
What You Are in the Dark: In the final battle, in which Luna is Fighting from the Inside, the Nightshadow tries to break Luna's resolve by pointing out that as far as the Mane Six know she's their enemy, and a traitor to the Realm. Her response?
Luna: That does not matter ...My future does not matter, beside the future of all Ponykind. And I stand by my kin, my friends — my beloved.