There are many types of bosses I capture from playing video games: power bosses, multi-stages bosses, army bosses, and puzzle boses. All of them can be designed to be bad or good.
The power bosses are typical bosses that rushes the player characters with raw power. They are very tough physically but the simplest to beat. These bosses serve the best as initial enemies where the player isn't yet getting used to the game mechanic, so there won't be a lot of a lot of strategy to beat them. However, if there are too many of these bosses, the game can become repetitive and dull. Bosses that take too many hit to die also are not good either.
The multi-stages bosses are bosses that invoke multiple forms or stage that create different battle patterns and there require different strategies to deal with. This type of boss is very common with final bosses, where the enemy mutate into multiple forms in attempt to beat you. Lavos from Chrono Trigger is one of the most iconic boss of this type, mimicing over 8 bosses inthe first form, and then has another two versions of the core unit you have to deal with. The best part is you can totally skip its first form. Neevertheless, too many of this kind of boss, however, will cause the battle to feel longer than it should.
The army bosses tend to appear along with the bandit and pirate tropes. They appear in the group of 3-8 units, with the leader sitting in the back row. Every turn, the mooks will zip away your health, argubly more than one power boss can do. You can't kill the mooks either because they'll just respawn, forcing you to focus fires on the leader and take him out before you're gradually bled to death. In my opinion, this type of boss is the most annoying, but alsp effective as the battle will set the villains up as gangsters or powerful strategists. I tend to feel very statisfy outsmarting these bosses in Lufia 3: The Legend Returns.
Lastly, puzzle bosses are bosses that require specific methods to beat. You can see these bosses a lot in Zelda and Titan climbing games: Hit here with this tool first, then climb there and slash the weakpoint. Rinse and repeat. In FFIV, there's also the Magus Sisters and the CPU that deploy units in the syncronized fashions you have to beat in specific orders to beat them. These bosses tend to be unique and very interesting to fight against, but they also can become annoying if there are too many of them.
In my final opinions, having many types of bosses in one game is a good idea. You can have variety of bosses from from the straightforward power contest ones to the strategic ones. It helps the player not getting bored easily.