I moved this to the correct forum area, but here I go with my answer, granted, I could probably think of more better ones if I had a way to remember every single one, but for now I'll go with this one, since it's still fresh.
What game had your favorite boss encounter?
Undertale
What boss was your favorite?
Asgore (pacifist run)
Why was it your favorite boss? (Mechanics, Lore, Music, etc)
Honestly, it's because of how the entire game is setting you up from the start that makes it amazing to me. The very first friendly monster you encounter tells you to avoid Asgore, because he will kill you. Then from there out, every single person you become friends with tells you the way to get home, while you keep hearing murmurs about Asgore. As the game progresses, you hear more and more about him, people praising him as their King, saying how he's the most kindest monster they know, he'd never hurt anyone, and how he's a great friend to all basically. The only issue is, as you're stuck in the land of monsters, and they're all sealed down there too, and the only way to break the barrier is with 7 human souls. So when you finally encounter Asgore, the first thing he does in the fight is smash your mercy option off your bars (Which if you're playing a pacifist run, is your key option basically). He's extremely hesitant while fighting, he obviously doesn't want to fight yet continues to do so to free his people, yet you're now unable to spare him, because he broke that option literally right off of your menus. There's a lot of deepness here that I'm missing out on honestly, but hey, the fight has great music too.
https://www.youtube.com/watch?v=Eqypnw6gQNg
Was this boss a challenge for you?
Honestly, the biggest challenge was just figuring out that you actually have to fight him, since up until then, if you're playing pacifist, you either delay everyone until they get tired of fighting and give up (Using the Mercy Option), or just run. Since Asgore breaks that, there really is no loop hole, you have to fight him.