The Mongols aren't that tough to beat if you play your cards right. Just have to build ports in the right places (to expediate troop deployment to key strategic choke points) and bottle them up on Kyushu. The hardest part is repelling the second wave from the mainland (Honshu). If you accomplish this and keep them limited to northern Kyushu, they eventually aren't able to expand, which means they don't get very many reinforcements. I think that's the key--limiting their expansion so they don't raise any revenue. Preventing them from winning battles also keeps their generals from gaining honor (you don't want any to reach 4 stars, and you don't want to lose your generals that have 4 or more ...). Once you get your production machine going it's all over for them (Yari Sams from Yamashiro, Yari Cav from Shinano, No Dachi from Satsuma if you can hold onto it, Archers from Totomi, etc.).