  We derive the classical analog of the extended phase space quantum mechanics
of the particle with odd degrees of freedom which gives rise to
(N=2)-realization of supersymmetry (SUSY) algebra. By means of an iterative
procedure, we find the approximate groundstate solutions to the extended
Schr\"{o}dinger-like equation and use these solutions further to calculate the
parameters which measure the breaking of extended SUSY such as the groundstate
energy. Consequently, we calculate a more practical measure for the SUSY
breaking which is the expectation value of an auxiliary field. We analyze
non-perturbative mechanism for extended phase space SUSY breaking in the
instanton picture and show that this has resulted from tunneling between the
classical vacua of the theory. Particular attention is given to the algebraic
properties of shape invariance and spectrum generating algebra.
