  We construct a nonlinear version of the d=1 off-shell N=8 multiplet (4,8,4),
proceeding from a nonlinear realization of the superconformal group OSp(4*|4)
in the N=8, d=1 analytic bi-harmonic superspace. The new multiplet is described
by a double-charged analytic superfield q^{1,1} subjected to some nonlinear
harmonic constraints which are covariant under the OSp(4*|4) transformations.
Together with the analytic superspace coordinates, q^{1,1} parametrizes an
analytic coset manifold of OSp(4*|4) and so is a Goldstone superfield. In any
q^{1,1} action the superconformal symmetry is broken, while N=8, d=1 Poincar\'e
supersymmetry can still be preserved. We construct the most general class of
such supersymmetric actions and find the general expression for the bosonic
target metric in terms of the original analytic Lagrangian superfield density
which is thus the target geometry prepotential. It also completely specifies
the scalar potential. The metric is conformally flat and, in the SO(4)
invariant case, is a deformation of the metric of a four-sphere S^4.
