Anti-Climax Boss: Everyone of the not-Elite Four final bosses of the GBC game are obsessed with playing their signature legendary cards who are clearly in the Awesome, but Impractical zone. The issue is that the energy cost for these cards are so crippling (6 energy cards attached to a single card, plus requiring a coin flip to do only decent damage?) and the AI prioritizes giving them energy over anything else, to the detriment of any useful cards in their deck.
The Computer Is a Cheating Bastard: Every single move in the games is planned out by the computer in advance, so reloading and trying a turn with a coin flip won't change anything. This also means the computer will deal out starting hands that will make the matching totally Unwinnable and there is nothing you can do about it.
Game Breaker: In the first game, the electric Grand Master has a deck of all electric types, meaning they're weak to fighting (except his Zapdos, which resists it). Since fighting includes ground ttypes which resist electricity, an all-ground deck could take him out (slowly) with little to no danger (until Zapdos comes up, in which case you'd better have one that does at least 40 damage).
Murray, leader of the Psychic Club in the first gameboy game. His deck is based around Stall, playing key monsters such as Chansey and Snorlax to soak up damage with their massive HP pools and using Scoop to return them to the bench with out losing energy. On their own they can just take attacks or attack, but Murray can also use Alakazam's Pokemon Power to transfer any damage he takes to any of his benched Pokemon(Like Chansey or Snorlax). Even worse, Murray can use Pokemon Center to heal all the damage you've manged to inflict on his active and benched Pokemon. Losing to him because of a Deck Out is very possible.
Bernard, leader of the GR Fire Fort, in the second game boy game. His "special rule" is easily one of the most unfair in the game: Fire type Pokemon have no weaknesses! Why is that so unfair? Well, unlike the other masters' rules, there's pretty much no way to possibly use this to your advantage, since his deck doesn't have any Water cards to hit your Fire types' weaknesses. So basically, it's just The Computer Is a Cheating Bastard disguised as a rules change. His deck is by no means bad either, and with no weaknesses to exploit the only real strategy is just to play really, really well. Or hope his A.I. Roulette gets handed the Idiot Ball.
Woolseyism: Occasionally attack name translations differ from the main video game series' to better fit the context of the card game move's effects; for example, "Nenriki" (literally "willpower") is "Confusion" in the video games (it has a chance of confusing the opponent) and "Psyshock" in the card game (it can cause paralysis).