I'm not sure about the best boss fight, most of them are pushovers that feel epic.
The GBA games have the best pre-final boss fights. FE6 dude (I forget his name, it's been a while), Nergal, and especially Lyon. The problem comes with the final boss, who is either a pushover (see Idunn), Comes out of literally nowhere (see random Fire Dragon), or just kinda make the plot a little worse (see Demon King).
I've only played RD in the Tellius series, but Ashera was kinda neat. I didn't like the Ike can only kill mechanic, or more accurately the way it was implemented. At least with Duma, who is decent in his own right, his health didn't regenerate to full when you tried to kill him with a non-main character unit. Thankfully, I knew that you shouldn't kill Ashera with another unit going in, but had I not it would've been maddening.
Awakening's Grima was pathetic, beat him with literally only Robin and Chrom in my R/C solo of the game. But, the atmosphere was great, with that amazing song in the background.
Fates bosses, oh boy these guys. Birthright's Garon, thing, was dumb and a pushover. Anankos was dumb, and an interesting boss since it accommodated FE being a game where you focus on multiple targets. Takumi was, admittedly, kinda cool, and a decent challenge (or at least his map was).
That's another important aspect of a final boss, their final boss map. The Fire Dragon has an awesome final boss map, with all of the villains getting cool morph forms, and you get awesome weapons.Or Takumi's which forces you to move forward quick or be crushed. Or Duma's, which is a boss rush. All of these add to the boss, making it cooler when you kill them, instead of Grima, where you literally just blitz him (you don't even have to give Robin the final kill to get the good ending, which would've been a nice call-back to Ashera/Duma)
So to put it into three neat lists.
Story-Wise, the bosses go as:
Ashera
Takumi
Duma
Demon King
Idunn
Grima
Garon
Fire Dragon
Anankos
Gameplay-Wise, the bosses go as:
Duma
Takumi
Ashera
Anankos
Fire Dragon
Demon King
Idunn
Garon/Grima (both equally bad)
Final map wise, the bosses go as:
Takumi
Fire Dragon
Duma
Demon King
Ashera
Anankos
Garon
Grima
Idunn