You need to be more specific about what mini-boss and what Zelda game. However, there is a mini-boss within each dungeon, providing a useful item after defeat. I would recommend using walkthroughs for more details.
a fourth monkey, and the mini boss. then more monkeys and the boss.
deffet the monkey mini boss
you find all the monkeys
a white monkey with a golden mask
Yes. He is the mini boss in the water temple.
You finish off the forest temple mini boss
You get it in the sky temple when you beat the mini boss.
battle the mini boss at city in the skys
Kill the mini boss on the Sandship
The boss key can be acquired in several different ways but usually you will acquire it in a chest. If not this method then you usually must defeat a mini boss.
Just wait.
The ball & chain? You have to beat the mini-boss in the mountain mansion place.