This will make the game more challenging and interesting. It gets repetitive when enemies and bosses do the same thing over and over, so I think this could add more tension and challenge (like I already mentioned) to the game.
For example, make a boss activate some sort of a force field or barrier when you try to get close to him. Or make a boss move according to your position on the screen.
If you have any more examples you came up with, please let me know in the comments! I’d like to hear it.