Horribly, HORRIBLY averted in Part V, which is like a fight scene out of Kill Bill.
Big Damn Heroes: In order of appearance - Rikku, Hitomi, Tifa, Rinoa, Cloud, and Hayabusa. It's gotten to the point where only one fight so far had a definite winner, because nobody showed up to interfere.
Bloodier and Gorier: The first four parts are relatively light-hearted compared to Part V. Before that Monty Oum made a point that "the girls were having fun", in a sort of supernatural badass training exercise, by animating their faces rather light-hearted. We're pretty sure that Tifa stopped having fun when she became a human pincushion.
Bottomless Magazines: We don't see her load new clips, but every so often a distinctive lock and load sound is heard between her barrages, coupled with an animation of Yuna sliding both guns near her hips for a brief moment. Her Gun Magic attacks, on the other hand...
Bullet Hell: Several of Yuna's special moves invoke this.
Rikku vs. Ayane. Promo shots suggest that they'll be fighting in some kind of underground base.
Kairi goes for Rachel, but when Rachel eludes her, she ends up by herself. The WIP footage from part VIII shows her transforming into Naminé to go up against Hayabusa and Momiji, with an assist from Vincent Valentine.
Rinoa vs. Rachel. We don't know much about what will happen to them, except for a shot of Rachel in chains.
Chain Pain: The ninjas in Part V attempt to subdue Tifa with chains.
Charles Atlas Superpower: Hitomi again. Everyone else has blatant superpowers, either through Materia or ninjutsu, whereas Hitomi is just very strong, very fast, and really, REALLY good at fighting. Good enough to outfight Tifa, who was loaded up with Materia and pretty clearly portrayed as the second most powerful combatant in Part II after Rinoa, using nothing but Wing Chun.
Tifa may have materia, but she primarily fights with her ungodly strength as well, and once deprived of the materia, she continues to devastate most of her opponents.
Subverted again in Part V, where individual ninja mooks go down like tenpins, but enough of them can push Tifa to her limits far more than any single fighter we've seen. Judging by what little we see of Kasumi's fight it went down in a similar way.
Diving Save: Rikku pushes Yuna out of the way of a flying block in Part I.
Do Not Touch the Funnel Cloud: The tornado doesn't seem to affect the fighters at all unless they actually touch the funnel cloud. Of course, since they're apparently made of indestructium, all the funnel cloud does is pick them up for some cool midair fight scenes.
While no match for him, Tifa can apparently do a split kick and a jump kick almost simultaneously.
Rikku does some after Tifa casts Hastega.
Namine also performs this move while maneuvering around Momiji's attacks and catching one of the Keyblades that was knocked away during her final attack.
Foe-Tossing Charge: Tifa, while on a platform, literally picks up one of the ninja standing between her and her target and hurls the poor Mook over the railing. Three more try to restrain her with chains and get tossed around like ragdolls.
One-Man Army: Tifa in Part V, and this is while bleeding from multiple wounds and suffering more as she goes.
Only a Flesh Wound: Tifa takes several sword cuts with visible blood sprays in part V and isn't slowed down in the slightest and even after having a sword stuck through the upper arm, is still able to use that arm just fine. And then there are the arrows.
Panty Shot: Several in I and II, though a few have to be freeze-framed to be seen. In III and onward, Monty seems to be moving away from this, unless he can't avoid it.
Interestingly, even though we got a quick upskirt just shortly beforehand, Kairi in one obvious frame doesn't have any underwear on. Possibly an animation slip-up, possibly not.
Popularity Power: The DOA team suddenly being able to go toe-to-toe vs. fully-levelled Final Fantasy characters is a subversion, since if you go by fandom backing Team Final Fantasy should be winning by a landslide (and they kind of do during most of Part II). In Part V's live screening you can hear everyone cheering for Tifa and quite a few people wondering who Hayate is.
Second Hour Superpower: Hitomi being able to punch the materia out of Tifa at the end of their fight, but not at the beginning. Why can she USE said materia immediately, without being told how? Anyone's guess.
Set Swords to Stun: Almost everyone is being blasted in the face with magic. How are they still standing exactly?
The opening sequences for Parts III and IV are shout outs to the ones from FFVII and FFVIII. IV's is also a shout out to Kingdom Hearts II.
In Part V Tifa takes a page out of Cloud's book and while being surrounded jumps onto a passing train.
In part II, Hitomi almost perfectly emulates Daigo's epic tournament victory from Third Strike against a hasted Tifa. Even the "parrying" sound effect is used (but instead of comboing into the win after parrying Tifa's attacks, Hitomi gets flipkicked in the face, and eats a Final Heaven shortly afterwards).
In Part III, right after the rather lengthy opening credits "When Angels Cry" comes up on the screen as the soundtrack from Devil May Cry 3 starts.
Based on what little we've seen of Naminé in previews and promotional stuff, it looks like she's gonna be borrowing some moves from Nu-13. The ending of the preview, complete with Vincent Valentine beside her, makes it look like she's channeling Xehanort from Kingdom Hearts: Birth by Sleep.
Ayane's ninjutsu, particularly when she does a series of hand signs before smashing the tower, borrows the "jutsu use" sound effect from Naruto.
Soft Glass: Tifa just smashes through a window at full speed and keeps on going. Mind you, this is Tifa we're talking about.
Theme Music Power-Up: A side effect of the fact that Monty actually builds his movies around the songs and not vice versa. The biggest comes in Part V - right after Tifa's flashback, the gentle music suddenly jolts back to life, and Tifa goes on a bloody rampage.
Rinoa was already fairly powerful in Final Fantasy VIII, being a Sorceress and all, but she was still just a powerful spellcaster. In Part II, though she goes full-on Valkyrie, complete with sword, shield, and wings.
Tornado Move: Dead Fantasy II. During the fight on the ice, Rinoa Heartilly creates a huge tornado that sucks all of her opponents into itself.
Victory By Endurance: Hayate adopts this tactic in Dead Fantasy V, by having his ninja assault Tifa after she's been beaten and severely weakened by Hitomi. Hayate doesn't attack until she's on the brink of exhuastion; having expended her remaining energy dispatching all but two of his squad.
We Have Reserves: A possible explanation for why Hayate lets his ninja fight against Tifa, dying in the dozens, eventually weighing her down with numbers. And he does that in spite of the fact that he can down her at pretty much any time he wants, since she was already tired from fighting Hitomi.