Measuring the mixing phases of the $B_s^0$ mesons is crucial to validate the $CP$ violation paradigm of the Standard Model and to search for new physics beyond it. Golden modes to measure these quantities are those governed by tree-level $b\to c\bar{c}q$ transitions, that allow precise and theoretically clean determinations to be performed. In addition, measuring the mixing phases with modes receiving major contributions from penguin diagrams open the possibility to reveal new physics appearing in the loops. In these proceedings we show the most recent measurements of $B_s^0$ mixing phases at LHCb.