Demonic Spiders: The Arachnemon, with all their status effect moves, are a Demonic Spiders in more ways then one.
Game Breaker: Any Digimon with the 'Heroic Move' ability will have an instant statistical advantage over one which doesn't but has the same or slightly better stats in multiplayer gaming.
All Elements make the Digimon take 30% less damage from all attacks. Status Barrier makes the Digimon immune to status ailments. As all Digimon can learn all moves in the game, having these two abilities together will have an absurd advantage over everything else. So much, that in high-level play, players are restrained on how many Digimon with those abilities they may take into the fight.
Evasion Dance, coupled with Parry Ring b (equipment), makes any Digimon incredibly hard to hit. To counter this you are obliged to have something with God's Eye.
Royal Slash is the strongest attack in the game, so much that in most rulesets you are allowed to have only one Digimon with it. It hits the enemy thrice, each time doing extremely high Holy damage.
Apocalymon, the Big Bad from the first season. He not only has Status Barrier AND All Element, as he also has Economizer, which reduces the MP cost of all of his moves, plus Skill Master, which increase the duration of status effects, which are game breakers on their own. His Signature Move hits all the three digimon of the opposing team regardless of their positions, deals high Dark damage and has over 90% of chances of causing Confusion, which halves the chance of successfully attacking (and this will last longer because of Skill Master). Equipped with defensive items and having one healing move, the opposing team has no chance of winning unless it is built specifically to beat Apocalymon, and if it does, it will be a ridiculously long battle.
Chronomon is arguably equal to Apocalymon at least. He has Status Barrier, Economizer S and All Elements, as well as Gods' Eye to counter Dodge Dance. He also comes with the game's best HP recovery technique as standard, and is resistant to Royal Slash.
To be honest, this could apply to Imperialdramon Paladin Mode and various other Digimon. The beauty of it is there are so many they almost cancel each other out. Gaia Origin and the Tamer challenge where you fight the cast of Digimon Savers are catalogues of Game Breakers, and even they don't cover all the candidates.
Unlocking DotShineGreymon at the beginning of the game gives you a Digimon that can easily slaughter most opponents, at least at first.
Even in competitive play, DotShineGreymon is difficult to beat; he has Status Barrier, Economizer S and All Elements, as well as Heroic Power. DotMirageGaogamon, on the other hand, has the first three and Heroic Move. It's also easy to set him up with a move which can revive other Digimon without having to DNA Digivolve. He's actually banned under certain rule sets.
Genius Bonus: Most of the locations are named after computing terms (Access Glacier, Macro Sea, Palette Amazon etc.)
Hilarious in Hindsight: Almost nine years after these two games were made, rival series Pokémon announced their new games, Pokémon Sun and Moon, which have a very similar motif.
"Stop Having Fun" Guys: Subverted. While there were attempts to create tier systems and standardised rules when the games were released in America, these quickly fell apart. A few rule lists are used, but there's no single example which all players follow.
That One Boss: A staple in the series. Among other things, GranDracmon gets multiple turns before each of your Digimon because he is absurdly fast, has more HP than all your Digimon combined, has an attack that will hit at least two of your Digimon for high damage, and occasionally inflicts bad status on you. Unless you're carrying the Legend set or have done massive grinding to that fight, you'll most surely struggle to take it down, IF you can take it down.
In Dusk, a mission that would be available way later for Dawn players will pop up in the request counter somewhere near the half of the story. In that mission, you have to defeat both Myotismon and Venom Myotismon. The first will go down with a couple of attacks and can't do much unless you're weak to Darkness. The second, however, will be way faster than your Digimon, a so high defense that your attacks rarely will do more than 5% of his HP, and has a skill that hits one of your digimon three times for high Darkness damage AND paralyze you should you survive the blow. Every turn of yours will be for healing or reviving one or two digimon and attacking with the two, or sometimes only survivor.
And even if you find both of them fairly easy, there's Imperialdramon Paladin Mode.
And after him, you have to fight Chronomon Holy Mode.
That One Level: Access Glacier and Macro Sea. While most stages will split up into different paths one will soon lead to a dead end. Not these two stages. Go one route take a fork, get some equipment, take another fork, get more equipment, take another fork, dead end, back track. Also, while most stages contains several types of Digimon to get their base experience these contain mostly water base, meaning you'll max it out instead of something more useful, like Holy or Dragon. Oh, and to fully explore the stages? You need to simultaneously go through both of them!
Shadow Hell also qualifies, but mostly for the missions that are done there. It is a very annoying maze with several dead-ends, and in all of its missions you're required to talk with more than one digimon. Thing is, Digimon B will only appear after you talk with Digimon A, so a unadverted player may pass throught the place Digimon B will appear, find it empty, then find Digimon A and wander during a long time fighting the random battles assuming that Digimon B area will be empty. One mission, especially, requires you to talk with THREE digimon and again with the first. Not only the aforementioned problem will make it very confusing, as Digimon A will actually change his position after you beat Digimon C. An in-game map would have made this much easier, but no, they couldn't even give us that much.
Loop Swamp has all the problems of Macro Sea, while also including one-way teleporters that give no hint or warning about where they go.