  Using the N=4 superspace approach in one dimension (time), we construct
general N=8 supersymmetric mechanics actions for the multiplets (b,8,8-b)
classified in hep-th/0406015, with the main focus on the previously unexplored
cases of (8,8,0), (7,8,1) and (6,8,2), as well as on (5,8,3) for completeness.
N=8 supersymmetry of the action amounts to a harmonicity condition for the
Lagrangian with respect to its superfield arguments. We derive the generic
off-shell component action for the ``root'' multiplet (8,8,0), prove that the
actions for all other multiplets follow from it through automorphic dualities
and argue that this hierarchical structure is universal. The bosonic target
geometry in all cases is conformally flat, with a unique scalar potential
(except for the root multiplet). We show that the N=4 superfield constraints
respect the full R-symmetry and find the explicit realization of its quotient
over the manifest R-symmetry on superfields and component fields. Several
R-symmetric N=4 superfield Lagrangians with N=8 supersymmetry are either newly
found or reproduced by a simple universal method.
