I like boss battles with phases. Where the game play switches slightly as you play, so you have to deploy a different technique. I also like it if one of those techniques is something that is only recently learnt!
I also like it to be a challenge. Not impossible, but something that you go away feeling like you have achieved something.
They also should be relevant to the plot. I play a lot of JRPGs, and, for instance (as it happens a lot with them) in Final Fantasy VIII I liked the giant robot boss as you escaped the missile base, as it was relevant to the plot... I also liked the return of that boss, even though it was a reduculous story point, at least it made sence. What I don't like are things like the Oilboyles underneath Balamb Garden... They come completely out of the blue, arn't linked to, or even mentioned in the plot and are just before another, actually relevant plot. The only purpose they have is to slow the gameplay down so that the delve beneath Balamb seems more epic than initially thought... They fall in with another sin... Bosses that turn into normal bad guys later... I know it can be a good way to show how much you have progressed, but really? It undermines that boss, and makes it less of a special moment when you finally destroy it. More often than not the regular enemy version has different stats and attacks anyway, so why don't they just make it a slightly different monster? Why is the enemy that is only found living in a pool underneath Balamb Garden also found wondering the hallways of the final castle?
I also like it to be a challenge. Not impossible, but something that you go away feeling like you have achieved something.
They also should be relevant to the plot. I play a lot of JRPGs, and, for instance (as it happens a lot with them) in Final Fantasy VIII I liked the giant robot boss as you escaped the missile base, as it was relevant to the plot... I also liked the return of that boss, even though it was a reduculous story point, at least it made sence. What I don't like are things like the Oilboyles underneath Balamb Garden... They come completely out of the blue, arn't linked to, or even mentioned in the plot and are just before another, actually relevant plot. The only purpose they have is to slow the gameplay down so that the delve beneath Balamb seems more epic than initially thought... They fall in with another sin... Bosses that turn into normal bad guys later... I know it can be a good way to show how much you have progressed, but really? It undermines that boss, and makes it less of a special moment when you finally destroy it. More often than not the regular enemy version has different stats and attacks anyway, so why don't they just make it a slightly different monster? Why is the enemy that is only found living in a pool underneath Balamb Garden also found wondering the hallways of the final castle?