Bosses that get weaker as you fight them
In most games it's pretty standard for bosses to get faster/stronger/ more aggressive with their attacks the closer you get to defeating them usually they'll activate some rage of the gods mode or break out supermoves. This can make the fight more fun and add a variety by giving them new moves and keep a challenge as well as being annoying depending on whether you have to take it from the trop each time you die or if the boss has checkpoints in the middle of it
What I rarely see is the other extreme. Bosses that show signs of injury and fatigue as you wear down their health. The only two examples I can name off the top of my mind are Sif from dark souls and Pious Augustus from eternal darkness. Who both start limping towards the end of the fight Sif even trips over which makes them seem more human/sypathetic and makes you feel like your attacks are actually having an effect.
Any other examples you can think of?