MGS1

Definitely the Sniper Wolf battle with the Grey Fox battle a close second. The battle itself against Sniper Wolf isn't hard even on the hardest difficulty, but the storyline along with the music is magnificent and brings a tear to my eyes every time.

MGS2

To be honest I wasn't that pleased with any of the boss battles in this game so i'm going to include a semi-boss battle which is. Snake and Raiden Vs the Tengu Soldiers, I loved this battle not only was Raiden fully clothed but I was fighting along side Snake while wielding a ninjato blade and also having to cope with GW going crazy. It's a shame it doesn't last longer

MGS3

The Boss, beautiful setting, amazing music and only 10 minutes to defeat her. Of course the time limit is only a problem on your first playthrough she is easy defeated in less than 5, however the ease of this battle doesn't change the fact that it's visually stunning and alot of fun to CQC your master.

An honourable mention goes to The End's battle as well, it's truly unique and has several movies for the different outcomes, you can also skip the battle by killing him earlier or even by putting the time forward on your console. Lots of originality much like the Psycho Mantis battle.