This is a really tough choice to make. I'll pick from my favorite games.
In terms of challenge, any one of those Green Golem bosses from the Mega Man games tend to be extremely difficult especially in Megaman X 5, which may not be a great game in comparison to other Mega Man games but damn, is that boss difficult.
Because it is one of my favorite games of all time, the ending fight with Kefka, while not challenging (if you have leveled up and do not place limits on yourself like I do) was very fun to play. You finally get to take on that madman!
But my favorite fight of all time, hands down is:
Metal Gear Solid 4, versus Liquid Ocelot. The final scene leading up to this last battle was shot beautifully and the emotions of the actors coupled with the tension between the characters created the perfect final fight that I had been waiting for since Metal Gear Solid 2.