The Biggest Threats:
This pokemon was such a big threat before that I had to get my own simply to not automatically lose to it. I need to be careful to get Primarina in safely and to preserve it against any enemy that might have this since it's my only reliable answer. Primarina often comes paired with more big threats such as Magnezone or Braviary on Kukui's roster, or Mawile on Xio's roster.
Outspeeds Greninja and OHKOs Kommo-o, hits monstrously hard, especially if it traces Protean. Scizor is the best answer to it, 2HKOing with Bullet Punch and OHKOing with Bug Bite. Unfortunately, there will be cases where you have to let Alakazam trace Protean, and if it does so then it will do a fuckload to Scizor with Focus Blast, and will also resist Bug Bite if it uses that move.
Can TWave through Mat Block, dodge Close Combat with Bright Powder or survive the hit with Sturdy, kills Primarina with Thunder and does a lot to Scizor with it, also potentially limiting your switching ability. A Magnezone + Alakazam lead pair would be an absolute nightmare.
Big Threats:
Talonflame4, Crobat3, Braviary3, and Tsareena4 more specifically. They all outspeed Greninja and OHKO Kommo-o, which makes the first turn quite hectic. My team has no flying resist, so swapping into any of the three birds above is challenging to do without taking heavy damage. Ice Beam + recoil from Flare Blitz/Brave Bird + another Ice Beam KOs Talonflame, Ice Beam is a 15/16 roll to OHKO Crobat, and Braviary is an 11/16 roll. Tsareena will sometimes HJK into Greninja so it's harder to neutralize without taking much damage. It also blocks Bullet Punch for the field, which can let fairy type partners tear through my team.
These are all grouped together since they're immune to Soulblaze and have some special tool to fuck up my team.
Togekiss: TWave is unpredictable and devastating, not OHKOed by Ice Beam or Bullet Punch.
Whimsicott: Tailwind, can damage through Protect with Twinkle Tackle, set 4 survives Ice Beam and +1 Flamethrower from full HP, both sets survive Bullet Punch.
Mawile: OHKOs every member of the team. Kommo-o is the best answer to it, so keep it alive and healthy on trainers that carry this menace.
Mimikyu: Annoying to kill thanks to Disguise and Rocky Helm, but with a decent damage output you can't ignore it.
Aromatisse: Sets TR. Not OHKOed by Bullet Punch, Aromatic Mist can turn Primarina34 even deadlier by making them not 2HKOed by Energy Ball, Heal Pulse is never fun either.
Shiinotic: Effect Spore punishes Scizor, not OHKOed by anything, although a few attacks are rolls. Spore is also a humongous pain in the ass to play around.
Smaller Threats:
Garchomp3 is neatly handled by Ice Beam + Protect in most cases, but it still deserves a place on the threatlist for how it restricts what you can do.
(Possibly) Immune to Soulblaze, can set Light Screen, can possibly stop Mat Block with Taunt or a Thunder(bolt) paralyze. Never attacks Kommo-o though so that's nice. OHKOed by +1 Close Combat, but be wary of Static.
Can stop Mat Block with Thunder(bolt) paralyzing, can also flinch with King's Rock. OHKOed by Bug Bite.
TWave, Bulky as hell, can trace Protean, hits fairly hard, and generally just a pain.
The three most notable TR setters. Audino gains a fairy type upon mega evolution which complicates things as it doesn't always mega. It also has a fire move for Scizor. Carbink can't touch my backline but can hurt the front quite a bit. Slowking hits fairly hard and is generally bulky and annoying.
Scarf Guillotine goes before Mat Block and OHKOs, however, this usually goes for X-Scissor.
Zapdos2 is incredibly hard to stop once it gets going since the best wall for it also has very little PP.
QC is never fun, this is no exception. Can also pack Thunder Wave or Memento for crippling.
No easy way around the Red Card since if it uses Baneful Bunker it still gets chipped by Soulblaze and swaps Kommo-o out. I also can't hit Water/Poison types very well.
Crit Sludge Bomb kills Kommo-o, however it almost always goes for Thunderbolt into Greninja. I generally use Mat Block to prevent a possible Dazzling Gleam from set 3
While every Rotom form is KOed by Dark Pulse + Soulblaze, Rotom-fan has an unpredictable scarf set that can Thunder and Air Slash it's way through the team.
These are the scariest Fake Out users, the others don't have the offensive presence to really be scary. Fake Out either stops Mat Block or Soulblaze, and there's no way to know who it'll target as it seems like an even split between Kommo-o and Greninja. I can't really offer advice on how to get around it as the scenario changes greatly depending on the other lead pokemon.
Hypnosis bypasses Mat Block, Fire Blast roasts Scizor, and Greninja can't do much to it. On the bright side, Energy Ball doesn't do shit to Primarina.
While it is Scizor food, Ninetales1 can set up Veil and Hypnosis my team.
Like Toxapex3, these have Red Card. However, they're rare and more forgettable so it's more likely that they erase your boosts by surprise
The main reason for Overcoat on Kommo-o. Spore from this guy can ruin the game, and beyond that it can use Rage Powder, Clear Smog, and more to ruin your day. On the bright side it can't touch Scizor, and using Grass Knot with Greninja on it's partner makes Spore and Rage Powder useless.