The damage certainly looks repairable - mainly because the motherboard designer was smart enough not to put thin inaccessible stuff around the battery.
First thing would be to clean up the corrosive mess still there. If you can still see blue-green, it's still eating away at your board. The opinions are divided on whether to use an acid (vinegar) to neutralize the alkali, or whether just to use distilled water. I'm in the former camp, I don't trust pure water to get it away, so I use cleaning vinegar, more specifically, I use toilet/kitchen paper soaked in the stuff and stick that on the affected parts for a few hours. Usually when I subsequently wash it away it takes all the mess with it.
Then it's a matter of determining the damage. You should measure with a multimeter (the kind with buzzer to show continuity are the best, but anything that can measure resistance is good enough) to be sure. Things look bad around the power connector, but those are BIG joins and probably only superficially affected. With a bit of luck only that one long, thin trace on the back is actually damaged to the point of needing repairs. If so, just get some thin wire and solder it to either end of the trace. Use sticky tape to keep it in place, both while soldering and later when in use. You're lucky nothing seems to have gotten into the ISA slots or under the SIMMs, or worse, under any big ICs.
Depending on how the rest of the solder joins look IRL it might be interesting to re-flow the big pins on the power and keyboard connectors, and possibly also the legs of those tantalum caps.