Whats the best way to clean stains off/out of a large rolling cooler?

I'd give a water/vinegar mix in a 50/50 ratio a try. If you need something stronger you can try a baking soda paste on the stains first followed by the water/vinegar mix letting it sit for 5 minutes followed by scrubbing with a stiff brush.

Do this outside. wash out, then fill with water/dish soap/bleach solution. Let sit overnight. Rinse thoroughly with hose. Dry inside of cooler. Store with lid slightly ajar. Use a magic eraser on outside.

Spray bleach cleaner on any and all areas that needs things to be removed. That would work wonders,along with a little abrasive scrubby and elbow grease.

Spray Scrubbing Bubbles with Bleach name brand cleaner all over it. Be sure to do this outside. Use a scrubbing brush or scrubby pad to scour it where it needs it. Hose it down and dump out all the water and let it dry in the sun.

Put some veniger and baking soda in and fill with hot water