To me, a good boss battle starts with a dramatic, fearsome enemy that looks impossible to beat, and maybe smacks you around a few times (or a few dozen) but then, through learning its attack patterns and phases, you get the sense of accomplishment from triumphing over it.
I think interesting patterns are one of the key components to a good boss encounter. I think the best bosses have the elements of a puzzle (I don’t think bosses that are ONLY puzzles are particularly good, because they feel cheap.)
Surprising phases are important, too. I have a love/hate relationship with phases, because I hate the feeling of white-knuckling to the end of the first phase only to be completely stomped by the second. However, the feeling of learning a new phase, and completely steamrolling through a phase you used to die on to the end of a fight is immensely rewarding.
For me, bad boss fights are either static (smack it until it dies) or obscure and needlessly punishing. A boss fight that just wants to kill you and doesn’t teach you anything meaningful is not “challenging” in the right way, just frustrating.
Some of my favorite games with boss fights are Panzer Dragoon games, Bloodborne, some of Yoko Taro’s games (Nier Automata, some of the Drakengards) and boss-focused games like Shadow of the Colossus, Cuphead and Jotun.
So for a while I’ve considered one of the biggest things to avoid in a boss battle is the “avoid the pattern and hit the weak spot” fights. I think good examples of this style is a lot of the bosses from Axiom Verge, specifically Uruku, or Little Horn from Super Meat Boy. These battles usually feel like rote attrition instead of a tense fight. I never finished Guacamelee because of it’s terrible final boss.
But when I thought about it, there are bosses that I love that kind of fit into this. Kraid and Crocomire from Super Metroid kind of fit into this. Both of those bosses, and frankly a lot of 2D Metroid bosses, end up being kind of a war of attrition with the beast. But what I think is the difference between these fights and the kinds I dislike is the fact that these bosses move and attack like actual creatures. What I mean by this is that, rather than just repeating their move set until they die, they react and attack in random and sometimes reactive orders. This makes sure the fight doesn’t feel like a repetitive obstacle barrage, but an actual fight. I think this is a major key to making a fun boss battle.
I think boss battles need to balance difficulty to avoid being pushovers or frustrating brickwalls, too. But beyond tedium and difficulty, I’m finding myself having trouble finding an essential quality to great boss battles. A lot of people are commenting on the “Exam” Model for boss battles, which I would usually agree with, but there are some awesome boss battles based around gimmicks, like the Stallord fight in Twilight Princess. (Honestly, a lot of Zelda boss battles might fit this!) Sure, you’ve been playing with the Spinner for a lot of the dungeon, but you pretty much never used the Spinner outside of this dungeon. So in a weird way, I think it’s less about focusing on the essential mechanics of your game, and more about avoiding introducing a new kind of challenge that the player isn’t prepared for. This is why games that aren’t really built for boss battles often have the worst ones. The SHODAN fight in System Shock 2 is pretty dreadful because that kind of combat is something you’ve never really engaged with in that game.
I’ll have to think about what I think makes a good boss fight for me a little harder, tho
Anyway I didn’t pitch in earlier so here’s some of my favorite bosses/games with bosses:
- Ridley from Metroid Prime, shout out to my girl Samus
- I just finished Hollow Knight so the final fight from that game is quite good, also worth mentioning the Hornet fights and the Hive Knight
- The End from Metal Gear Solid 3, also the Boss and the Fury are great! Probably the only game that’s made a stealth game with good boss battles.
- Ornstein & Smough from Dark Souls because c’mon
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Okami has some really good bosses but I haven’t played it in a while
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Darkest Dungeon also has some really challenging and cool boss battles
Also are mini bosses still bosses??? Debate
What really makes a good boss battle is the difficulty, I had some experiences in some games where the minions are actually harder to kill than the boss! not cool!
I like bowser in super marioi 64 becuase of that, he is really difficult to beat! would love to get some replies 
