snakeisninja: Kaiba that son of a bitch gets the best cards AND the best music in the damn game! He gets a theme song, his own duel music, and variations of the first two for his future self! AND THEY ALL KICK ASS!
The entire soundtrack in general, which is the one nigh-unanimously praised aspect of the game, and a big motivation for players to play through the Campaign mode to hear all the game's tracks (and to play through Campaign again after beating it instead of just playing Free Duel, as Free Duel uses its own single music track across all opponents instead of the game's various tracks heard in Campaign).
After you make it past the preliminaries in Kaiba's tournament, you'll duel Shadi, the fifth opponent overall. While the previous four opponents scaled up in difficulty, Shadi is a noticeable step down, having monsters with stats in the hundreds, and not having significant fusions nor magic/trap cards in his deck. He's pretty much the only opponent past the early game you're guaranteed to not need to grind for besides the Mage Soldier.
When you return to the past, the first mandatory opponent is the mage soldier, whose monsters only have stats in the mid thousands, as well as no significant fusions nor magic/trap/equip cards. He's much weaker than the past few opponents you dueled in Kaiba's tournament, as well as the opponents to come.
High Mage Secmeton of the sea shrine and High Mage Martis of the desert shrine. Secmeton uses a whole deck of water monsters, the strongest of which, Crab Turtle and Suijin, only have 2500 attack each, alongside the Twin-Headed Thunder Dragon, thus you can beat him just with your own Twin-Head without any equips, especially as the Sea field powers it up. Martis uses powerful fiends and spellcasters for his main attacking force, that while still strong, do not get powered up by the Wasteland field; this results in him fielding significantly weaker monsters than what the other high mages are using against you, and leaves him reliably beaten by an unequipped Twin-Head.
In the endgame gauntlet, Sebek is much easier than the high mages you dueled previously, as well as easier than the opponents to come. He uses machine and beast type monsters, with the strongest being Metal Zoa, whose 3000 attack is old hat by this point, and dueling him on a Yami field does nothing to boost his monsters while it can be utilised by you (especially if the player has Skull Knights and Zoas in their deck). Most of his remaining monsters only have slightly more than 2000 attack, and he has no significant magic/trap cards nor equips beyond Shadow Spell.
Complete Monster: Heishin is an Evil Chancellor and Evil Sorcerer of Ancient Egypt. As soon as he gets the ancient power of the Millennium Items, he attacks the palace with his soldiers, killing various people, including the Pharaoh and his wife, and mortally wounding Simon Muran, the Prince's tutor. When the Prince tries to escape, he threatens to kill him if he doesn't give him the Millennium Puzzle. The Prince shatters it, and is transported inside of the puzzle to the present day. When he returns, he finds that Heishin has destroyed much of Egypt and Simon Muran has died from his injuries. After defeating Heishin's top mages, he finds Teana has been kidnapped and is having her life threatened in an attempt to lure the Prince into a trap to kill him, but this is stopped by Seto, Heishin's own henchman, who sets her free and ends up being The Starscream. Heishin obtains the Millennium Puzzle and summons the Dark God, Darknite, and commands him to destroy the world and make him a god, to which Darknite responds by killing Heishin. Petty, selfish, and so obsessed with power that he'd attempt to murder underage teenagers in his pursuit of it, Heishin was a monstrous individual.
Critical Dissonance: This game often gets criticized for its brutal difficulty and the amount of forced grinding needed to get pass certain areas. Despite this, it's treated rather warmly by fans who played it back in the day, and is currently listed as the fifth game of the top ten PS1 games on GameFAQs, despite barely having over a 50% review rating.
Cult Classic: Despite being infamous for its brutal difficulty (or perhaps because), this game still has quite a bit of fans to this day.
Ear Worm: The main battle music for the Kaiba tournament arc of the game. Part of the reason that part of the game is treated as one of the games high points, despite introducing a rather nasty Difficulty Spike, is because of that song.
The Meadow Mage. He's just a mook you only see on one screen in the game, yet he's the character that's remembered and talked about the most. With his amazing card drops, including giving most people their first Meteor Black Dragon, people have fond memories of extensively dueling him and gaining the cards that allowed them to finally beat the game.
Because of just how useful it is throughout the game, even people who play the real life card game have a fondness for Twin-Headed Thunder Dragon. Helps that its real life counterpart was one of the easiest fusions to make back in the day in the real card game as well.
The Meteor Black Dragon never appeared in the anime/manga except for a single appearance in an early movie that was never released outside Japan and a single appearance in Yu-Gi-Oh! GX. Additionally an official card of it wasn't released for the TCG outside Japan until 2012, over 12 years after its OCG release, and long after the TCG's Power Creep and arrival of better Red-Eyes fusions rendered it obsolete. However with its status as the Infinity+1 Sword of this game and being the key to beating the game for every player, it has a deity-like reputation among those who played Forbidden Memories, like the Twin-Headed Thunder Dragon example above.
Franchise Original Sin: If it's true that this game uses beta-rulings for the actual game, then it shows that special summoning was always supposed to be a big part of the game, or at least, Fusion was. In fact, thanks to being able to get the cards out quicker due to not needing poly and being able to chain fusions, Fusion Monsters in this game are far easier and quicker to get out than the later introduced Synchro and Xyz monsters, one of the most criticized aspects of the game from the old-school purist.
Game Breaker: The magic card Raigeki, which destroys all of your opponent's monster cards with no cost to you. A single Raigeki can break a stalemate and win you the duel in just that turn, and just like any other card, you can have three of them in your deck. Having multiple Raigekis can be vital to surviving the endgame, especially if you don't have any Meteor Black Dragons. In addition, most of the time, you will start the game with one already in your deck, making it immediately useful right from the start.
The equip card Megamorph; it's not only compatible with every monster, but it'll also boost their stats by 1000. It'll turn any midtier monster into a powerhouse, and the most powerful monsters will become untouchable in all but the most extreme circumstances. You can get it as early as Pegasus too, that is if you're good enough/patient enough to S-Tec him many times.
Goddamn Bats: Labyrinth Wall and Millennium Shield; they have no attack at all and thus will never pose a direct threat to you, but they have a massive 3000 defense that will require equip and magic assistance to overcome unless you have the Meteor Black Dragon out. They're additionally Uranus-aligned, and the Saturn alignment is rather uncommon. Once you get to the finals of Kaiba's tournament, most of the opponents from that point on will have one or both in their decks until the endgame gauntlet.
Older Than They Think: Seto's encounter and battle themes are remixes of a tune from Monster Capsule Breed and Battle, a Japan-only game.
Scrappy Mechanic: The starchip system, due to most strong and useful cards being absurdly expensive for how little starchips you win from duels, along with the fact so many cards are given a 999,999 cost to make them unrealistically buyable. The only real use for it is buying a few "steals" that managed to slip through the cracks (such as Jirai Gumo, a 2200 attack and equip-versatile monster that only costs 80 starchips due to its 100 defense, and Millennium Shield, a 3000 defense monster that only costs 200 due to having no attack, and is unwinnable from dueling).
S-Tecing. If you want to get any of the actually useful magic/trap cards and those very valuable equips, you have to get S/A Tec ranks in your duels for those cards to drop. Generally you have to either make your opponent deck out or have the duel go on to near decking out while using a lot of magic, traps, and fusions. So to get a S-Tec, you have to stall duels out, while trying to exploit the AI into doing more card combining than you or getting in as many magic/trap/fusion activations as you can. A single S-Tec duel can take about an hour to complete. Then you factor in that the chances for getting the good cards still aren't that great.
Tear Jerker: The Prince's sealing in the Puzzle is sad, especially with what Simon says.
Simon: One day, when the Puzzle is solved, you will be free to walk among men. Until that day comes... Sleep, my prince.
When you return to the past, you find Egypt has been completely overrun, the Prince's parents are dead, and everything you knew of your old life is in ruins. The music is also really sad.
The Blue-Eyes Ultimate Dragon. It's by far the most powerful monsters in the game with 4500 attack, 750 more than the next strongest monster, and 1000 more than the Meteor Black Dragon. It requires three equips at minimum to defeat through battle, and only three obtainable monsters can do it with three equips. And due to the 1 card-per-turn limit, using Raigeki or another magic card to destroy it can leave you open to a direct attack, including to another Blue-Eyes Ultimate Dragon.
The next strongest monster, the Gate Guardian, can be this until you get multiple Meteor Black Dragons. It has 3750 attack, is highly equip-versatile, and is used by a disgustingly large amount of opponents in the game. The Gate Guardian's threat diminishes greatly if the player gets some Meteor Black Dragons, as they can beat the Gate Guardian without equips when sun-aligned.
Raigeki, being a Game Breaker as covered previously, works just as effectively at nuking your playing field.
Shadow Spell, which reduces the attack of all your in-play monsters by 1000, crippling them unless significantly equipped. The card Curse Breaker can be used to reverse its effects, but having no effect beyond this and being the epitome of Useless Useful Spell, you won't be having it in your deck, much less having in your hand/on the field when you actually need it.
Reverse Trap reverses the effect of equips, leaving you with a crippled monster, and killing your chance at a comeback if powering up that monster was your only hope to overcoming your opponent's overwhelming forces.
Swords of Revealing Light, which prevents you from being able to attack for three turns. While it can be just an annoyance, it can lead to your opponent building up a force or drawing the magic/equips needed to take your monsters out without retaliation.
Megamorph, which powers up any monster by 1000 points. If it gets used on an especially powerful monster, the duel is likely over unless the player draws Raigeki and can immediately regain control the next turn. Unlike the other non-Reigeki examples here, it can be legitimately obtained by the player, though it's difficult to win even if you know who to S-Tec to get it.
Dragon Capture Jar. While Pegasus is the only one who uses it consistently enough to be a threat, it can destroy every dragon on your side of the field, including Meteor B. Dragon. This becomes even worse if you're trying to S-Tec him with a strong monster, as the most powerful monsters in the game are dragons.
If you're not prepared for him, Seto 2. He has plenty of 3000 ATK cards like Metalzoa and Black Luster Soldier, and his strongest monster is, you guessed it, the Gate Guardian. The weakest monsters in his arsenal have over 2000 attack, and if you do get something strong he'll Crush Card or Raigeki you. He's also at the end of a difficult labyrinth without the ability to save, meaning if you lose you'll have to fight the Labyrinth Mage again.
High Mage Kepura is the most difficult of the high mages you'll face, and is as difficult as what you'll face in the endgame, using Gate Guardian powered up by the meadow you duel him on. With an attack over 4000, it'll take just two direct attacks from it to be defeated. Additionally, if given the opportunity, he'll often equip his Gate Guardian to make it even more powerful. Even the Meteor Black Dragon alone won't gain you victory here.
Seto 3 is also this, being the most difficult opponent in the game, having Blue-Eyes Ultimate Dragon (at an even higher frequency than the final boss) and nearly every other extremely powerful monster, as well as a very high frequency of using Raigeki, Shadow Spell, Widespread Ruin, and Harpie's Feather Duster (while the final boss uses no magic cards at all). Plus he has the ability to see your facedown cards and thus can't be bluffed. Also, unlike every other opponent in the game, Priest Seto is smart enough to place Raigeki on the field before placing a monster so he can defeat you on his turn.
Pegasus. By the time you face him, even with grinding, he'll still have some really good cards at his disposal, one of which is a Meteor B. Dragon as well as three (and sometimes four) Raigeki. He also has Dragon Capture Jars in a game where dragons are your main fighting force. True to the anime, he's programmed to be able to see what cards are in your hand, as well as what cards you have face down, making him impossible to bluff. There's a reason he's considered one of the hardest bosses in the game... On top of that, he gives some of the best magic and traps in the game, meaning you're going to be fighting him a lot in free duel. Granted, by that point, you should have far better cards to face him with, but he can still prove to be a massive pain even then.
Unwinnable by Insanity: When trading with another player, you're not required to put up the same amount of cards the other player is trading (nor have to put up any card at all). As such, it's possible to trade all your cards in your chest, and while the game does not allow you to trade cards that are in your deck, the game does not disallow you from exiting the build deck screen with less than 40 cards in your deck. So if you were to trade without 40 cards in your deck, and traded enough cards away, you would not have enough cards left to fill out a 40 card deck. And since you can't have 40 cards in your deck, the game will not allow you to duel anyone, thus preventing you from being able to get more cards.