Your Sim's high school grade also affects the chances of getting a distinguished degree offer. A and B improve chances, C has no effect, D and F reduce chances. Does not apply to Sims made in CAS as YA or older.
Sims can also improve their chances of getting a distinguished degree offer by flaunting fame or donating to the university, but those carry a risk of failure which will reduce chances instead. Check the phone's Work menu after you've applied to find Flaunt Fame and Give "Donation" to University. These commands only appear if your Sim has enough fame or money to use them. I'm not sure what the requirements are.
Best skills for Biology are Fitness, Gardening, and Logic. Wellness and Veterinarian also help.
Best skills for Fine Art are Painting, Photography, and Violin. Piano and Pipe Organ also help. (Guitar skill doesn't.)
