Cities: Skylines

This can be achieved by hitting the goals listed in the campus overview panel. It will give you three goals to hit by the end of the academic year: total academic works, campus attractiveness, and total students.

Attractiveness: This can easily be done by just building one of each of the buildings as they unlock. Make sure to build a few dorms spread throughout the campus and try to build residential around them as well. Ultimately you want to be able to have a student limit of 5k or more, for other achievements.

Students: Make sure to turn on all of the policies for the campus and ensure you have a high student capacity. You should be able to get this no problem so long as you have proper access for your residents to get to the campus.

Academic Works: Basically turn on your research each year and max out all funding and staff. There are a few choices for research, but they will all typically bring in anywhere from 2-5 world per year and I believe the max you should need is somewhere around 12-16 total. You will ultimately need 100 works across all campuses to get another achievement.

Prestigious comes right after acclaimed status.

Please let me know if there is anything I can add or change to help make this solution better.