That may be the plastic, itself rather than paint. MoldingMolding the parts using colored plastic and a mold with a mirror finish produces a surface like that.
Getting that kind of finish with paint basically requires "polishing" the paint. It is sanded with extremely fine sandpaper (grit in the thousands), then polishing compound, and buffed. It'sIt's essentially the same process as painting a car.
If you need to do that with small parts, do the painting process as you've described. IfIf there's a lot of surface detail, skip the sandpaper. YouYou can use toothpaste as polishing compound. WhenWhen you buff it, don't let the surface heat up, as that will melt the paint and make the surface a mess. CarCar bodies have a lot of metal to suck away heat, but plastic is an insulator and heat will build quickly.