The rules in the individual level speedrun says, no bosses, any ability can be brought into the first level. What does it mean by no bosses?

It looks like you've misread, it says you can

Sorry look at my comment I fixed it

it means you stop at the level before the boss, so you don't do the boss fight for the run

In Kirby: Nightmare in Dreamland you can only challenge every boss (except of DeDeDe and Nightmare) once as they get replaced by the door that leads to the next world. Therefore it is only required to finish every level as it is simply not possible to beat the bosses again.

Oh ok thx I'm looking forwards to speedrunning this on my gba lol