Is it a popcorn ceiling? If so, you might be better off scraping it all off and respraying it.
Yes, I believe that is what the ceiling is called. I can’t even take the duster to it it seems
Can you share a photo of your ceiling? TSP will do the trick in most cases. If it is a popcorn ceiling, and why would there be a popcorn ceiling in a kitchen(?), you would be better removing it and starting over.
Ok, that's not bad. Looks like an orange peel or modified stipple. TSP and a car was sponge will work just fine. Just so you know, you can't paint over grease, you must wash (with TSP or any degreaser), let dry, then prime, then paint. Or the paint will fail. Since you will be working overhead and on a step stool, wear eye protection, you don't want to get any splashes in your eyes. Safety first.
It is very difficult to wash a textured ceiling. You may have to repaint. You can use a primer first to seal in any stains.
ok. That’s what I was kind of thinking!