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Just use all your mana on ying-yang. Nothing else. Do not waste Money getting Terracotta Army or ArrowRain, since you do not need it.
Basically you should have ying-yang researched ying-yang when the rocketeers arrive and be able to get 4 more directy (after that as soon as you got enough mana for the next one). Just build monkeys and warriors all the time, and of course buddahs as soon as the spot is save to build. With that you should be able to finish the level and I think when i managed to get the achievement even 1 rocketeer died. But there where still enough left.
For Chinese 9, you'll have to abuse the Mind Control and Yin-Yang spells on the Sun Giants. They are tough enough against the Boulders the Aztecs can throw at you. The Shield spell is helpful if the Sun Giants has to take down their towers.
Oh, and be sure to establish Buddhas as you get closer to their base. They will prevent the Boulder from destroying anything beyond them, but they will be destroyed themselves. If that happens quickly build a new one in its place! The Mind Control and Yin-Yang spells are expensive on the Sun Giants, so it's very important to have as many Buddhas for the mana regen.