  When electrons populate a flat band their kinetic energy becomes negligible,
forcing them to organize in exotic many-body states to minimize their Coulomb
energy. The zeroth Landau level of graphene under magnetic field is a
particularly interesting strongly interacting flat band because inter-electron
interactions are predicted to induce a rich variety of broken-symmetry states
with distinct topological and lattice-scale orders. Evidence for these stems
mostly from indirect transport experiments that suggest that broken-symmetry
states are tunable by boosting the Zeeman energy or by dielectric screening of
the Coulomb interaction. However, confirming the existence of these ground
states requires a direct visualization of their lattice-scale orders. Here, we
image three distinct broken-symmetry phases in graphene using scanning
tunneling spectroscopy. We explore the phase diagram by tuning the screening of
the Coulomb interaction by a low or high dielectric constant environment, and
with a magnetic field. In the unscreened case, we unveil a Kekul\'e bond order,
consistent with observations of an insulating state undergoing a magnetic-field
driven Kosterlitz-Thouless transition. Under dielectric screening, a
sublattice-unpolarized ground state emerges at low magnetic fields, and
transits to a charge-density-wave order with partial sublattice polarization at
higher magnetic fields. The Kekul\'e and charge-density-wave orders furthermore
coexist with additional, secondary lattice-scale orders that enrich the phase
diagram beyond current theory predictions. This screening-induced tunability of
broken-symmetry orders may prove valuable to uncover correlated phases of
matter in other quantum materials.
