Wangan Midnight Maximum Tune 2 has Sonoda, who you race twice in Story Mode, on stages 10 and 55. Good God, this guy loves to block you, often causing you to run into a barrier or traffic car in the process. Even in Maximum Tune 3 onwards, which makes Story Mode much easier, he's still an asshole compared to other opponents, so he still counts. And if you lose, he mocks you by telling you that "your style is boring."
And 30 (which is usually the toughest one). Still even that's a walk in the raceway park compared to 59, where 1. you face Akio and Tatsuya 2. on the shortest course they race 3. which ends at one of the most technical sections in the entire game. It will take you a while to win this stage. A long, long while. (This may also qualify as a Wake Up Boss stage, as it takes places amidst one of the easiest blocks of stages in the game.)
In Diddy Kong Racing you have Wizpig. Every boss in the game is exceptionally tough, but you're given boost balloons, zipper panels, and missile balloons to get ahead of the boss. Then comes Wizpig. His course lacks any upgrades and every person who has played the stage agrees that while you can mess up maybe a few times you can beat the other bosses, but doing a single thing wrong at any point during the race against Wizpig is the same as a forfeit. This means that you must play perfectly. This also requires using any tricks in the game, exploiting the boss's ability to kick you forward, and hidden stats in all the characters making it impossible to beat with most of the cast (something that doesn't necessarily guarantee a loss against any other boss). Even by the already extremely harsh standards of Diddy Kong Racing, this boss is difficult beyond so. The remake fixed this however, as Wizpig has magically fallen out of shape it seems and now runs slower than you drive.
After beating Wizpig, then you have to race a rocket version of him. While the rocket is actually slower than Wizpig on foot, there's the slight problem of you being in the middle of a Macross Missile Massacre and/or flying through extremely narrow passageways. Getting hit by anything has a pretty strong tendency to throw you off course, and landing in front of a pillar means the race is essentially forfeit. See how bad it is, and note especially the room at roughly 1:15.
And after that you see the credits and think it is over, right? Wrong. There is a second mode which plays all the courses backwards, so good luck learning how to race him again.
Before all of that is the boss of the third world Bubbler the Octopus who is formidable in his first race where he drops mines around the course, but becomes outright infuriating in the rematch with him where he now drops bubbles made to temporarily hold you in place while he gains a hefty lead over you if you get caught in the bubbles. Even the strategy guides say that he is the hardest boss by far, and they really aren't kidding.
If you don't take him out early, he can accumulate an insurmountable 10-second lead, driving the course perfectly. Some races, you never even see him, except off in the distance at the front of the starting line. Even if you manage to catch him with a power play or route changer, he can still slip past you with a fraction of a second to the finish line. If you guessed Raptor, from Split Second, you're correct!
blur has That One Objective: in order to unlock the final boss challenge, you need to maintain a speed of 125mph for an entire lap. Even the A-Class cars are hard-pressed to stay above 125 in hard turns.
F-Zero GX, one of the hardest racing games ever (try the story mode on normal, let alone hard or very hard), had That One Boss as level 7 in the story mode, the Grand Prix. You are on one of the most unforgiving tracks in the game, with lava pits and very few rails, and extremely sparse health. The difficulty comes from the computer giving the Black Bull (your main enemy) extra speed and also imbuing the rest of the NPC's a desire to murder you. Until this point, you've never faced very aggressive AI at all, in fact, you've been the one being aggressive with attempting to damage opposing vehicles. You are also used to only needing 1 hit to take out an enemy or at least put them very far behind you, but Black Bull will shrug off the first attack and FOR SOME REASON get a small boost which means you have to use precious energy to boost again to kill him. There are two ways to win: Either try to take out Black Bull at the beginning with two immediate hits (very difficult with everyone else trying to hit you and the random speed boosts given to him), or to survive the first lap, and then use boost more effectively than your opponents and race perfectly to stay just behind Black Bull and ahead of everyone else, with the hope that at the VERY END, you can purposely hit explosive mines to get enough of a speed boosts to pass him just before the finish line, of course without hitting too many or you die.
Normally, all the Ridge Racer secret cars are earned through very tough one-on-one races, but R4: Ridge Racer Type 4 is a little bit different. Earning cars works like this: you're given two choices for each playthrough of the main story: your racing team, which determines your sliding scale of speed vs handling, and your car manufacturer, which influences whether you use a Drift (classic Ridge Racer) or Grip (no drifting but a simplified turning mechanic). Each has a nationality: American, Japanese, French or Italian. If you're taking on the secret cars with a version with a mismatched nationality (e.g. the Italian manufacturer by way of the French team) then the secret cars aren't that tough to earn. However, their true versions when you match team nationality and manufacturer are something on the order of anywhere between 10-30 MPH faster than the mismatched versions, and faster still than you, and this is all if you have the best cars up to that point. They can be hell to complete, to say nothing of what it takes to earn a car that even comes close to chasing them down. To qualify this, R4 is a very unforgiving Ridge Racer title. Touching anything in the normal game will substantially slow you down while your flawless opponents whiz by you. Both handling styles demand great precision from you, or else you will crash into either sidewall or the completely-oblivious traffic around you. You have to nail almost every single turn in order to win races, especially the last four ones out of eight, where you're required to in order to advance. A perfect run on one track will only give you a good chance of winning a race. Imagine what precision it takes to outrun one of the "true" extra cars.
In the original Ridge Racer we have the end-game duel against the 13th Racing, later known as the Soldat Crinale, affectionately nicknamed by the fans as the Devil's race car. And that's a quite fitting nickname: you race on the Advanced circuit on the reverse direction, at nightnote And trust us, it's very difficult to predict the road ahead with such pitch-black darkness.. The Crinale will not start until you surpass him, and after a few seconds he takes you over again at an outrageously high speed. The car will then stop dead in its tracks to give you another chance of taking him, but after doing so, he will slowly rack up speed as you progress through the race. But do not, do NOT let him take you over or he won't give you another chance of recovering. And just to feed more fuel to the fire, the Crinale is painted completely matte-black (thus meaning it's very hard to see him as you race at night) and its position on the circuit is not shown on the map, thus means it's brutally difficult to predict his tactics. But win this race and the Crinale, the best car in the game hands down, is yours to keep.
Let's just say that all duels against these secret cars in all Ridge Racer games fall into this trope in one way or another.
Gran Turismo 4 has the final wet race around Tsukuba Circuit, in which you must race against one of the fastest cars in the game (typically a Toyota 89CV◊ or a Mercedes Benz CLK GTR), in ultra low grip conditions with the AI at it's highest difficulty. To top all of this off you get a five second time penalty whenever you collide with anything, be it the other car, a barrier, or any other obstacle you might face.