Regarding specific Asian ethnicities, here is a table from 2000 comparing educational attainment, among other things:
http://www.asian-nation.org/demographics.shtml
Percentage with college degree varies considerably. Compared to white people (25.3%), Indian (64.4%), Chinese (46.3%), Korean (43.6%), Filipino (42.8%), Japanese (40.8%) people had significantly higher percentage with college degree. Cambodian/Hmong/Laotian (9.2%), Pacific islanders (13.2%), and Vietnamese (13.8%) people had significantly lower percentages, more similar to Latino (9.9%), native American (10.8%), and black (13.6%) people.
Patterns of immigration presumably account for much of the differences. Some ethnic groups came heavily through PhD student and skilled worker visas, selecting them for high educational attainment, while others came in more through less selective (on educational attainment) methods. Once here, parental educational attainment relates to the nature and nurture that the immigrants’ American born kids have with respect to their own educational attainment.