Completing a neuroscience major?

What is it like completing a neuroscience major, particularly at a top tier are second tier university? What is the rigor like?

That’s too vague to know. “Rigor” is a pretty fuzzy term to begin with, and that can vary vastly depending on the specific university and program, the options you select within that degree (if you have choices), and your own personal strengths. I wouldn’t expect it to be a walk in the park, but I also wouldn’t expect it to be like skydiving without a parachute. That leaves a lot of space in between.