Mix (at a minimum, and increase as you see fit), a mixture of 1 cup Bleach to 1 gallon Water. Apply w/a scrub brush and let it sit for a few minutes. W/O rinsing yet, reapply a 2nd scrubbed-on coating, THEN rinse. Start from the BOTTOM, and work your way up to avoid streaks.
Be sure the room is well ventilated and that you wear gloves. The solution needs to 'sit' on the mold/mildew for a short time in order to KILL the stuff. As for the window ledge, wipe the mixture on and let it sit. I'm assuming it's a painted surface. These days, there are 'specialized' paints w/a mildewcide already mixed in for rooms, like bathrooms, where there is high humidity. If you're considering repainting the B-room, clean the walls w/the mixture, then PRIME w/a good Latex Primer/Sealer like Kilz, then paint at least 2 topcoats (of a paint w/Mildewcide already in it.)