You'll have to scuff up that mirror finish so something else will stick to it. Then get a metal primer. I've had good luck with Krylon spray primer for metal stuff, my kitchen cabinet hardware was done 18 years ago and has never worn nor chipped.

DTM (direct to metal) paints bond very nicely, as do etching primers.

Wet sand it with at least 600 grit to break the surface. The acid based primers work nicely, it isn't necessary to sand much at all - sanding until it looks like you've sanded the whole thing is way too much work. Use a finer grit after the primer, wet sanding again.

The reason for wet sanding is because the sandpaper stops working almost immediately when dry - it clogs. Because it is hard to find open coat paper in local stores just put a few drops of dish soap in the water.