We obtain the minimax rate for a mean location model with a bounded star-shaped set $K \subseteq \mathbb{R}^n$ constraint on the mean, in an adversarially corrupted data setting with Gaussian noise. We assume an unknown fraction $ε\le 1/2-κ$ for some fixed $κ\in(0,1/2]$ of $N$ observations are arbitrarily corrupted. We obtain a minimax risk up to proportionality constants under the squared $\ell_2$ loss of $\max(η^{*2},σ^2ε^2)\wedge d^2$ with \begin{align*} η^* = \sup \bigg\{η\ge 0 : \frac{Nη^2}{σ^2} \leq \log \mathcal{M}_K^{\operatorname{loc}}(η,c)\bigg\}, \end{align*} where $\log \mathcal{M}_K^{\operatorname{loc}}(η,c)$ denotes the local entropy of the set $K$, $d$ is the diameter of $K$, $σ^2$ is the variance, and $c$ is some sufficiently large absolute constant. A variant of our algorithm achieves the same rate for settings with known or symmetric sub-Gaussian noise, with a smaller breakdown point, still of constant order. We further study the case of unknown sub-Gaussian noise and show that the rate is slightly slower: $\max(η^{*2},σ^2ε^2\log(1/ε))\wedge d^2$. We generalize our results to the case when $K$ is star-shaped but unbounded.