These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Demonic Spiders: Deathbellows are probably the only Transgenant that will put the same fear in you as a Chryssalid would. I mean, Bees.MyGod.
Deathbellows, for those not in the know, are giant, hollowed out slug-things with bees in them. The bees are their "ammunition", meaning once they fire, you can't do anything about the bees themselves, which will always hit, and don't particularly care if you're wearing armor. One shot will half kill a soldier, if you're lucky (otherwise, they're dead). The bees are fired at a quite frankly ludicrous rate for the damage they do, and the Deathbellows themselves are resistant to projectile, laser, and explosive weaponry (i.e 90% of your arsenal). If you encounter a mission with Deathbellows, it's better to just abort and try again some other time.
As the indent above suggests, Deathbellows are surprisingly flammable though and their tendency to lay in wait around corners is easily their weak point as well. Once you have a trooper up to the highest possible speed, it's possible to scout around corners (carefully) spot there they are and then run back around the corner before they can react. At that point it becomes ridiculously easy to dispose of them using the prepared orders system to run around the corner, chuck an incendiary grenade near it, run back and wait till it's crispy.
Deathbellows are a lot easier to deal with in urban terrain types, because there's almost always some urban debris lying about that you can use as a shield to get close. Once you know where the Deathbellows is, switching to your designated grenadier, getting him/her close enough to toss grenades, and having him toss a few charges over the cover will quickly deal with the Deathbellows. On larger wilderness maps, you can afford to standoff outside the Deathbellows' firing range and wear it down with sniper rifle fire.
In Aftermath Reticulans packing plasma guns will feel this way in the early game. Lategame, substitute Microslug Accelerators.
Beastman Matriarchs in Afterlight can rapidly enter Demonic Spiders territory depending on how they are armed, and what you have on the field. You will particularly hate Plasma Cannon and lightning throwers if you're relying on drones.
You're generally going to hate Beastmen no matter what. They can almost always see you before you see them (especially during night missions), they have better range and accuracy than you do, and they absolutely love to chuck grenades at you. If you don't have Heavy Suits or Life Support Suits, you're going to die. If you do have Heavy or Life Support, you're looking at a significant healing time for your soldiers anyway.
Aftershock gives us Wargot Grenadiers. Their Frag Grenades are mostly harmless, but Incendiaries will put at least one of your soldiers in the sick bay for a while.
Also from Aftershock, the Starghosts. What makes them so dangerous is that they can use mind control to capture an entire country if you fail to defeat them when they attack a province. And you can never get the country back.Ever.
High-level Psionics have powerful psionic abililties that can affect the accuracy of your troops at best, or make them start shooting at their allies at worst.
Game Breaker: It's pretty safe to say that the late-game Ball-Lightning Launcher from Afterlight radically alters the entire game and brings down the difficulty level. Up until that point, the Beastmen are still terribly efficient opponents, and can only be defeated by carefully avoiding direct confrontations and using lasers and mind control properly. The Ball Lightning Launcher allows a technician/soldier with Driver Training to generate an explosive "Lightning Ball" that can be guided for any distance and any amount of time, and detonated For Massive Damage right in the enemies' faces. And since the launcher has an in-built thermal imaging sensor that can tell you about enemies around the lightning ball, you can pretty much win any mission with a single soldier, provided he's got enough batteries to power the damn thing.
In Aftershock, cyborgs who max HP boosting stats and implants have absolutely ridiculous health, more than any enemy can ever hope to overcome.