The parametric equations describe $(x,y)(t) = (2 \cos(t) - \cos(2t), 2 \sin(t) - \sin(2t))$:
In order to convert this into polar coordinates, express the radius, and the angle in terms of $x$ and $y$ first:
r(t)^2 = x(t)^2 + y(t)^2
this would be a simple expression in terms of $\cos(t)$. You could them express the polar angle using
atan2 as follows $\theta(t) = \arctan(x(t), y(t))$. The radial representation would be obtained if it were possible to solve for $t = t(\theta)$, and substituted into $r(t)$ to obtain $r(\theta)$. But the equation is not linear and does not admit a simple closed-form.
However, seeing that $r(t)$ is much simpler, we can invert it to find $t=t(r)$ and then $\theta(r) = \theta(t(r))$. Doing so will only allow us to parametrize half of the cardoid, due explicit symmetry $r(t) = r(2\pi - t)$.
If you permit the use of software, here is a way to get the radial representation: