To be eligible for a BSc degree at Govt. College, Shimla, Shimla, candidates must have completed their 10+2 education with a minimum aggregate of 50% in the science stream from a recognized board. Additionally, candidates must have studied subjects like Physics, Chemistry, and Mathematics/Biology in their 10+2 curriculum. Some colleges may also require candidates to clear entrance exams like JEE or state-level entrance exams. It is important for candidates to check the specific eligibility criteria set by Govt. College, Shimla, Shimla, before applying for the BSc program.