I work in Shanghai how can I apply a 12 mth multiple entry visa for my mom (we are Singaporean).

Has your mom been to China before? If not, it will be hard for she to apply for a 12-month multiple China visa.
I think your mom can apply for a dependant work visa to enter China, and then apply for a residence permit at the locla public security bureau within 30 days of her entry to China. later, shen can enter and exit China with the residence permit for unlimited times within it validity.