Essentially, when the boss is given similar, or the exact same, abilities as the player.
Slide 1: The SA-X in Metroid Fusion
Now, Samus is well known for being an ustoppable badass. But at the start of Fusion, she nearly dies as a result of her X-Parasite infection, and had to have portions of her armor removed and sent to the BSL station for study. But the parasites within the armor actually start mimicking Samus and breach its containment, kickstarting a massive outbreak. A good portion of the horror with the SA-X is the fact that it's mimicking Samus at full strength, while Samus herself is in no condition to actually fight it. So, it's essentially showing you what Samus is like from the perspective of her enemies, especially since Samus has become part Metroid herself.
Slide 2: Ganondorf in Zelda: Tears of the Kingdom
I know Dark Link would probably be the more obvious answer here, but this is my opinion. Upon getting to Ganondorf, you realize that he fights quite similarly to Link himself. For one, he uses all 4 of the same weapon types (one handed swords, spears, giant 2 handed weapons, bows) as Link throughout the battle. He even does his own versions of the spin attack and sword beam. Likewise, throughout the Wild-era games, Link can do perfect dodges to slow down time and open the enemy for a flurry rush. And wouldn't you know, Ganondorf can also do a perfect dodge, even getting the same slowdown effect as he does so. Finally, throughout ToTK, Link can summon the ghostly apparitions of the other Sages to help him in battle. In the second phase of the fight, Phantom Ganon fills the same role for Ganondorf himself.
Slide 3: Shizuka and Apollo in Crosscode
Crosscode is a really charming game set inside an in-universe MMORPG. The main character Lea belong to the Spheromancer class. Throughout the game, you meet Apollo and Shizuka, who are also Spheromancers. And sure enough, when you battle them, they have access to all the abilities Lea herself does. You can even learn how to do some really high-effort comboes just by watching the two of them.