  The discrepancy between Planck data and direct measurements of the current
expansion rate $H_0$ and the matter fluctuation amplitude $S_8$ has become one
of the most intriguing puzzles in cosmology nowadays. The $H_0$ tension has
reached $4.2\sigma$ in the context of standard cosmology i.e $\Lambda$CDM.
Therefore, explanations to this issue are mandatory to unveil its secrets.
Despite its success, $\Lambda$CDM is unable to give a satisfying explanation to
the tension problem. Unless some systematic errors might be hidden in the
observable measurements, physics beyond the standard model of cosmology must be
advocated. In this perspective, we study a phantom dynamical dark energy model
as an alternative to $\Lambda$CDM in order to explain the aforementioned
issues. This phantom model is characterised by one extra parameter,
$\Omega_{pdde}$, compared to $\Lambda$CDM. We obtain a strong positive
correlation between $H_0$ and $\Omega_{pdde}$, for all data combinations. Using
Planck measurements together with BAO and Pantheon, we find that the $H_0$ and
the $S_8$ tensions are $3\sigma$ and $2.6\sigma$, respectively. By introducing
a prior on the absolute magnitude, $M_B$, of the SN Ia, the $H_0$ tension
decreases to $2.27\sigma$ with $H_0 = 69.76_{-0.82}^{+0.75}$ km s$^{-1}$
Mpc$^{-1}$ and the $S_8$ tension reaches the value $2.37\sigma$ with $S_8
=0.8269_{-0.012}^{+0.011}$.
