If you want to rescue that board, you'll need to take off and replace/clean all the affected components, neutralize/scrub away the damage, replace components, and cover the exposed traces from scrubbing with something like clear nail polish. This is a great thread on the topic: https://pinside.com/pinball/forum/topic/stripping-battery-corrosion-with-a-strong-acid
If you go down this route, make sure to invest in decent desoldering and soldering guns.