  We consider the problem of recovering an unknown signal $\pmb{x}_0\in
\mathbb{R}^{n}$ from phaseless measurements. In this paper, we study the convex
phase retrieval problem via PhaseLift from linear Gaussian measurements
perturbed by $\ell_{1}$-bounded noise and sparse outliers that can change an
adversarially chosen $s$-fraction of the measurement vector. We show that the
Robust-PhaseLift model can successfully reconstruct the ground-truth up to
global phase for any $s< s^{*}\approx 0.1185$ with $\mathcal{O}(n)$
measurements, even in the case where the sparse outliers may depend on the
measurement and the observation. The recovery guarantees are based on the
robust outlier bound condition and the analysis of the product of two Gaussian
variables. Moreover, we construct adaptive counterexamples to show that the
Robust-PhaseLift model fails when $s> s^{*}$ with high probability.
