While undergraduate finance courses require only first semester calculus at most, PhD finance programs require strong mathematics and economics background. I started as a finance major with a math minor. After I made a decision to apply to finance PhD programs, I added the economics major to prepare myself to be competitive in this market. Below is a list of critical courses that you should take if you desire to gain acceptance into a tier 1 or top tier-2 school.
<Essential Courses>
Calculus I, II and III (up to multivariate calculus)
Linear Algebra
Micro Theory (maybe called Price Theory) courses (up to a master level course)
Econometrics courses (up to master level courses)
These courses will build the foundation of the coursework during the PhD program. You may reconsider going into a PhD program if you absolutely do not like these courses.
<Helpful Course>
Ordinary of Differential Equations
Real Analysis
Probability Theory
Mathematical Finance
(Intro to) Partial Differential Equations
Financial Economics
Game Theory (Good start for the corporate finance theory)
Macro Theory Courses (especially graduate level courses)
Applied Econometrics
Stochastic Calculus (If there is one: check both math and stats classes. If you are interested in Asset Pricing, this is a must.)
While taking these courses is critical, in order to be competitive you need to have a strong GPA. Most schools will not even look at your application packet if your undergraduate GPA is below 3.0 and master's below 3.5. Generally speaking, a strong candidate at least has a GPA of 3.5, and if you are applying top schools, most candidates may have a GPA of close to 4.0. If your overall GPA is weak, hopefully your quantitative GPA is strong.