I might try that one day, but it won’t be as simple as that. Even if you don’t leave via the window Paul dies if he so much as sees an enemy, and an MIB runs in through the door and opens fire as soon as the ambush starts.
Before you go in, you set mines around the doorframe to blow up the MIB that charges you. Then you can stay in the room and blast anybody coming down the hall, then move to the staircase and snipe the last guys hanging around the lobby.
I tag the lobby with gas mines as well. That keeps the troops coughing while your brother runs past.
yah, like not being able to jump across knee high fences in some fps…
In the very old PC RPG Battletech: The Crescent Hawk’s Inception (or something like that), you play a student at battlemech school who is out driving around in a school combat exercise when bad guys show up, invade the school, and destroy the mech you’re driving, which is a superpowerful one that is never ever available again in the game. Except that (as I discovered by accident the very first time I played it) you can flee from them and slip out cracks in the walls of the arena that you’re fighting in, and keep that 'mech for the whole game.
And, as I later deliberately discovered, if you try hard enough, you can actually beat the overwhelming force of bad guys fair and square.
In the '80s arcade wrestling game WWF Superstars I once clotheslined the Ultimate Warrior out of existence.
There were many bugs in various versions of Streetfighter II, most of them quite well known. One that I only saw once ever involved Blanka jumping in on Guile and, before landing, being simultaneously hit by a sonic boom and a spinning bunch. Blanka then ended up walking around in mid-air for a while.
I had Benoit beat Ric Flair and Hulk Hogan in a handicapped match. So that was nothing.
Not really “supposed to be impossible”, but like others posted here it certainly simplified things.
In Jedi Knight, the final battle is between your character (Kyle Katarn) and Jerec, the leader of the Dark Jedi. It is intended to be a to-the-death lightsaber duel. Jerec is effectively immune to every non-saber weapon in the game (he blocks it) with the exception of the satchel charges, but he still resists something like 90% of the damage done with those. During the duel, he runs to a “Force column” to heal up, plus drawing in some other columns to seal himself in (which makes you lose the game if you don’t stop them in time). Stopping the columns wakes him up, and he comes after you again. This is supposed to repeat three or four times until you actually kill him.
Well, while he’s in the Force column he’s floating and invulnerable (until you stop the other columns). But stationary, so placing 10-15 satchel charges at his feet is pretty trivial. Place them, stop the other columns, he comes out of his meditation and steps down right onto a megaton of high explosives.
Game over, win. 
I was also (once) able to physically block him outside the column as he tried to run back for a heal, allowing me to just beat on him, since the AI was stuck in “get to healing area” mode and he didn’t fight back. That one is probably more in line with the OP.
In Zelda:Ocarina of Time I started my save game only to discover that everytime I called for Epona (on the ocarina) I would hear her neigh and gallop towards me but she was invisible. Heard but not seen. Sadly couldn’t ride her either.
Turned off the game and restarted from the same save point and she was back to normal.
My brother beat Piston Honda in 6.66 seconds on the SNES (Super Punch Out). I think 
that’s really really fast, first time knockdown was a KO.
Not impossible but my claim to fame is completed Super Mario World with 93 worlds opened. The only three not opened being the 3 switch palaces. Hard but rewarding.
That was the only way I was able to beat that mofo, and it took me forever, and what an unsatisfying victory! Hmmph.
I did have a more satisfying “impossible” moment, though. The first time I played through Half-Life, I fell down a long passage, wantered through an old lab room, and took a corridor out into a huge cavern with a train-track in it.
And leapt back, as a huge beetle-like creature charged me.
It took me a long time, but I eventually managed to kill it, via placing proximity mines right at the entrance to the cavern.
Awhile later, I got stuck, and looked at a walkthrough for the game, and found out that these huge beetles were impervious to normal damage: you’re supposed to kill them (I think there are only two of them in the game) through mission-based goals. This one I was supposed to lead down between two electrodes and blow it up…in later replayings of the game, I never was able to replicate killing it through normal weapons.
Daniel
Are you talking about the Gargantua? Their armor makes them invulnerable to bullets*, but they can be killed by explosive weapons, such the grenade launcher, RPG, tripmines, satchels or even hand grenades.
*I’ve often wondered if a shot on one exact tiny area- the eye?- can inflict damage.
In Spyro II on the PS1, in Glimmer I managed to get up a ladder without having learned how to climb ladders. There’s a superfly powerup that’s just close enough to fly there instead. Not that it gets you anything particularly exciting.
In Ratchet & Clank, in Pokitaru there’s a particular spot at the edge of the map underwater where you can swim through the ground and keep swimming down. You eventually can swim into the Pokitaru sewer. Doesn’t really get you anything worthwhile, aside from having done it.