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: Literal ones. Well, they might not literally be demonic, but they're literally spiders, and they're certainly a big enough pest to make one think they came from hell. They appear right when the game's Fake Difficulty starts going through the roof. The game is full of them, though... practically every mook becomes a Demonic Spider after the first few areas of the game.
Game Breaker: Valsu's Elixir spell, which he gets at level 42. For 120 MP, it restores all HP and MP, essentially turning Valsu into a portable Trauma Inn. Keep a couple of MP restoratives on hand just in case, and you cannot lose.
Player Punch: Lemele was killed five years before the beginning of the game by Gorsia, who pretended to be him for you to help revive him. In the past, after defeating Gorsia, he kills you, but you are revived still in the past as a baby. The Baby's name is Lemele. You just finished the most Nintendo Hard RPG ever to find this out in the ending.
Averted with Lejes once you get the Star Rune, and/or Save Scumming with B-Protects. Lejes has a very odd AI; he will always cast Defense Down on you until your Defense is as low as it can be (1/2 your normal). Since the Star Rune raises Defense and is infinite, keep using it until Lejes misses with his Defense Down. Use a B-Power, and then keep using the Star Rune until he misses again. Defend. Attack. Pray you kill him with a double-hit. If you don't, repeat the process until you do. You cannot lose. Period.
Pretty much any apprentice battle aside from Wilme (who is laughably easy to defeat) heads straight into Puzzle Boss territory after making a wrong turn at Luck-Based Mission junction. The winning strategy in nearly every case is to find the right combination of buffs and healing spells/items that lets you survive long enough to one-shot (or two-shot) your opponent if the Random Number God is kind enough to allow you an opening. And because of the stat bug, raising your character's level actually makes these fights harder. This is why it's a good idea to get the Star and Sky runes as early as possible.
Another way to beat them is to note that they match the level of your main character and not that of your second party member. Kill off your main character, level your ally, and use them to fight the battle instead.