Not exactly sure what you mean by hardest game. The closest thing to a perfect game was played between Robert Byrne and Bobby Fischer. It's been called the Game of the Century. Every game of chess is won by someone making one or more mistakes. With Byrne and Fischer in 1956, both players played perfect moves -- if there is such a thing -- yet Fischer finds a way to win.
Hardest Game ever!!

How are they perfect moves then? Well, i suppose they could be perfect moves and he could have still got mated buttt....

Well, there's no such thing as perfection -- not even in chess. But there is no definite mistake made by either player. When I go over my own games, I see the turning point where I win or lose. Too often it's me hanging a rook or something silly ;)
But with Byrne and Fischer,it was book moves through the opening, strong middlegame play by both sides. I really can't see why Byrne ends up losing, but somehow he does.
Keres-Smyslov game with the un-accepted rook sac. Smyslov made a move missed by many of the best computers. However, it was eventually proven to be the only move. It was a very tense position.

There was the great correspondence player, Purdy. He played almost perfect chess. His games are amazing, but one must keep in mind that he had lots of time to think about his next moves. There's no such thing as time pressure in postal chess.
I imagine some of his victories would have to be considered the hardest in history. If I have no time pressure and I'm allowed to access books, just think how hard he had to outplay his opponents to win games like he did.

I believe a game of Kasparov Vs Topalov in somewhere between 1990-2000 was the best game of the century
Kasparov calculated so beautifully and so did Topalov, but Kasparov ended up winning, Kasparov SACRIFISED soooo much pieces and in the end came on top, tell me this isnt the most hardest game ever played and i will come to your house... and prove you wrong!
Some1 said "G. Kasparov - V. Topalov; Wijk aan Zee, 1999.
Maybe the most complicated game ever played. I spent six months analyzing what others had written, before even attempting my own analysis. Then I methodically compared my analysis to what had already been done. I probably spent over a year preparing the game before it actually appeared here on my web pages. A truly Herculean effort. (Analytically) This game features one of the most complicated combinations and "King Hunts" that ever took place in a real, over-the-board game. "

Yeah, I'm not sure what the hardest game is; maybe golf. In reference to the Fischer-Byrne game. It was the media coining it the game of the century..not that it was not a great game. Most programs now find better alternatives to the critical Byrne moves. In fact, many feel that Fischer was somewhat lucky with reference to the depth of analysis needed for the amazing combination that defined the game.

Yeah, in retrospect, the Byrne/Fischer game was a lot of hype, given Byrne the experienced player and Fischer still so young. Kids can play better chess than that now, and many kids beating experienced GMs is not unheard of at all nowadays.
For its time, it was a great game though. Theory has advanced by leaps and bounds though.
As for "perfection" (I know it doesn't really exist) -- are there games where neither side seems to make a mistake yet there is a clear winner???

Every time I see the Kasparov v Topalov game it reminds me that "yes, Garry was the best ever". So many of the moves he made were obvious moves that I would have made earlier, but each time he makes a precursor move that strengthens his position. Here he is having his pieces picked off of the table at a furious pace, and yet he has seen the future - he knows - Topalov is beaten. Just an awsome game.

Reshevsky vs. H. Mecking -- Tunisia, 1967
Another game with so much depth. Both players do so many amazing things, I can't even begin to comprehend it. There are many turning points where it looks like White is winning, then Black, then White, etc., back and forth with every move.
Even Fritz or any super computer would be impressed!
Hey what do you all think that the hardest game ever was? I have no idea