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.
The fact that quite a bit of the back story can only be found at the forums certainly doesn't help.
Demonic Spiders: Sneaks (A type of snake) are probably the most common, but they're getting edged out of their position as "King of all monsters that make players tear their hair out." The most obnoxious thing about them is that they're very, very difficult to hit with anything except a ranged attack unless your character has high dexterity. However, some more-recently-introduced monsters are just as hard to hit or worse, and they don't have the ranged weapon weakness. And since status effects were introduced fairly late, monsters that use them are really, really obnoxious.
Mighty Shadow Hydra have the ability to stack bleeding status effect which inflicts harm based damage whenever it hits you with its attack, and all of its resistances are lower than 100%. Bring it down to half health, and it summons its second head, increasing its damage output and bleeding, to the point that it can deal somewhere around 500 damage per turn. Put sinply, you need to handle it quickly before its damage output snowballed out of control.
Good Bad Bug: During the "Divide by Zero" war, the monster pool was abnormally strong, leading to waves of monsters that were 30 levels above the character's level. This also meant farming was made easier, but slowed war progress.
That One Boss: The "Unbeatable" and Void monsters are mostly designed as these.
The most recent example is the Shadow Storm, which is a big reason for its status as a Base Breaker. The way it works is, it starts the battle with a powerful 2 hit SP attack that randomly hit with light or darkness element, and it spent the next four turn to recharge its SP and HP until it can use its SP attack. Rinse, and repeat. Its SP attack also have an effect to reduce your damage output, and you have 25% chance to get stunned and do nothing. It actually have quite a low starting HP, but it have a much higher maximum HP which means it can regenerate itself until it have five times its starting HP if your offensive power are unable to compete with its massive hp regeneration.
Shadow Storm was even worse In its original version, because of a programming mistake which caused its damage output to be doubled, enough to outright one shot a fragile character if they are caught in the wrong armor set up. This bug have been fixed, and the Shadow Storm has been re-adjusted since the damage fix.