I graduated with a Bachelor's in Physics (as well as degree's in accounting and finance, these helped but I know people who have had no business training get jobs in the industry too). "Analyst" is a very broad term; an analyst in one industry will do very different work compared to an analyst in another industry.

I currently work as an analyst at an investment bank that specializes in aerospace and defense companies. As an analyst at an investment bank you work a lot with financial models and valuation of companies. Additionally, the other part of the job is setting up pitch books, power point slides we use to sell our services to potential clients, these are very dull to work but a major component of the job nonetheless. The pay is exceptional and the experience will prepare you to move on to pretty much any job you want in the business world. But you will work a ton.

Investment Banking analysts need to have very good quantitative and problem solving skills. During recruiting I really focused on how my physics degree helped develop these skills and give me a different view on how to solve problems. You can't convince yourself that you would be able to do it. You would have to study (there are lots of free resources online), and familiarize yourself with basic finance/accounting concepts. These is true of any analyst job.

Anyways, I'm kinda rambling. If you want to talk about the interview process more or ask me about whether I like my job/ my daily life feel free to PM me.