The senior accountant job title isn't for the faint of heart. Well, really, it's just not for those just starting their careers. Hence the senior title. This means you need to have some experience under your belt to secure a job under this title.
Once you have experience and education, you'll be ready to tackle the senior accountant world. That means you'll be doing everything from analyzing client account information to maintaining subsidiary accounts. On top of being able to do this work without supervision, you're also going to be in charge of a small accounting team. So you'll need to be ready to answer questions.
Quite generally, senior accountants become such after being a staff accountant with that firm for a few years. Many senior accountants recommend learning how to do your job above and beyond expectations so that you're already considered for the position before you've even applied. Some things are just that easy.