https://www.youtube.com/watch?v=TehsUGLsQv8 Look at minute 1:25
Judging by how Bonkers acts in that video, Smash Run bosses are going to be more like random events.
If you played city trial in Kirby's air ride then you'll probably remember the different events that happened during it, such as the Dyna Blade appearing, meteors falling, etc.
This Smash run bosses seem to be of that same kind, they spawn somewhere in the map and if you beat them you probably get a lot of power ups, but they don't seem to act like mini-bosses, but rather more powerful regular enemies, i say this because in a Kirby game when you encountered a Bonkers, you were caged in a scenario until you defeated it, however in this video the player can choose to ignore Bonkers and he just continues to walk normally when he is not attacking.
By this logic, having Mini Kraids and Krusha as those kind of enemies would make sense.