Just grind the crap back to bare metal cut out a piece of scrap car or any bit of sheet metal, pop rivet the piece in and repaint the area, should be mostly common sense.
It's not a structural part of the car so glue the patch on with araldite, fiberglass it, whatever, it matters little.
Fiberglass would be great for all doors, guards etc it don't dint, I'm sick of car park dints from those who don't care.
Just remove everything in the area and hose liberally with water to remove all the remaining acid before doing anything.
note; most rusted under battery areas are due to a faulty regulator allowing the alternator to boil the battery spilling acid, check the charging system also.