  Shape coexistence in the $Z \approx 82$ region has been established in
mercury, lead and polonium isotopes. Even-even mercury isotopes with $100 \leq
N \leq 106$ present multiple fingerprints of this phenomenon, which seems to be
no longer present for $N \geq 110$. According to a number of theoretical
calculations, shape coexistence is predicted in the $^{188}$Hg isotope. The
$^{188}$Hg nucleus was populated using two different fusion-evaporation
reactions with two targets, $^{158}$Gd and $^{160}$Gd, and a beam of $^{34}$S,
provided by the Tandem-ALPI accelerators complex at the Laboratori Nazionali di
Legnaro. The channels of interest were selected using the information from the
Neutron Wall array, while the $\gamma$ rays were detected using the GALILEO
$\gamma$-ray array. The lifetimes of the excited states were determined using
the Recoil Distance Doppler-Shift method, employing the dedicated GALILEO
plunger device. Using the two-bands mixing and rotational models, the
deformation of the pure configurations was obtained from the experimental
results. The extracted transition strengths were compared with those calculated
with the state-of-the-art symmetry-conserving configuration-mixing (SCCM) and
five-dimentional collective Hamiltonian (5DCH) approaches in order to shed
light on the nature of the observed structures in the $^{188}$Hg nucleus. An
oblate, a normal- and a super-deformed prolate bands were predicted and their
underlying shell structure was also discussed.
