A one-parameter family of trans-series asymptotics of solutions to the
Degenerate Painlev\'{e} III Equation (DP3E) are parametrised in terms of the
monodromy data of an associated two-by-two linear auxiliary problem via the
isomonodromy deformation approach: trans-series asymptotics for the associated
Hamiltonian and principal auxiliary functions and the solution of one of the
sigma-forms of the DP3E are also obtained. The actions of Lie-point symmetries
for the DP3E are derived.Comment: 102 page