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: For new players, the Fat Gangsters are going to be this. Their shoulder armor is highly resistant to physical attacks, so the reliable tactic of Hero Action, Jump, Shoot becomes ineffective. Unless you use Metal Coated Rounds, the way to win is to stay on the ground and attack from either the front or the back.
Also, any enemy with poison attacks, especially in dungeons, where the permanent damage to your life bar can really add up. Thankfully, you can be prepared for this, either by linking terminals that reduce/prevent poison to the dungeon, or putting Germ-Resistant Vests/Germproof Suits on everyone.
It's also worth noting that looking at how this game separates Direct and Scratch damage and the way Ravagers and Commandos work in FFXIII is very similar. And both feature action-oriented battle systems that have few options and simple commands, but are meant to be tactically complex. A fan of the game once said "It's like it does everything FFXIII did wrong correctly."
"Funny Aneurysm" Moment: Pater's hand-drawn comic book and heroic speech are seen in a far different light when the events play out and it really does "cost him his life."
Narm: The tower, Basel, has the same name as a city in Switzerland. This makes it very difficult at times to take things relating to it seriously.
Never Live It Down: Zephyr is "good in the dark". That's great for fighting, not so great when Leanne wants to slap you for peeping, and also not great for when Vashyron wants to make innuendos.
Game Breaker: An easily craftable item (Combat Scope ß) can be sold for more than it costs to make. Add into this that the materials to create it are readily available in another shop in Chapter 6 and beyond and you have the recipe for essentially infinite money.
Punch-Packing Pistol: Breaking your pistols is actually one of the main game mechanics. It doesn't show on the models, but in the inventory screen you can see your pistol decked out with ridiculous stuff like a drum magazine for absurd amounts of ammo before having to reload (really good, since you unload one cartridge with every attack), scopes stacked on top of each other, and multiple handles for decreased recoil.
Squick: Thinking about just what that steak Barbarella is eating is made of. Hint: It doesn't have four legs and you killed it yourself. Although you do get dog meat later on as Vendor Trash, which is slightly less squicky...
Tear Jerker: We dare you not to get a little choked up by the events of Chapter 13.
That One Boss: Cardinal Lagerfeld. Made worse by the fact that it's preceded by about 10 minutes of cutscenes with no chance to save afterwards and that you'll need a lot of trial and error (or a guide) to know which equipment to take (you can't change equipment without reverting to the pre-cut scene save). Also, you only have one character. Lagerfeld can teleport to get you behind cover and has a one hit attack that can completely drain the hero gauge.
Wangst: While Zephyr's flashbacks do make his withdrawn nature more understandable, his threatening of Juris with a gun — who the team had just made a huge effort to save — and screams of "why can't I die!?" are more than worthy of a few cringes.