  Phase and time delays of atomic above-threshold ionization are usually
experimentally explored by the reconstruction of attosecond harmonic beating by
interference of two-photon transitions (RABBIT) technique. Theoretical studies
of RABBIT rely on the perturbative treatment of the probe (NIR or visible)
laser pulse with respect to the atomic electric field and the pump composed of
a train of attosecond pulses made of several harmonics with frequencies
multiple of the probe fundamental frequency. In this work we present a
semiclassical non-perturbative description of the phase delays for the emission
of electrons from hydrogen atoms based on the strong-field approximation as the
relative phase between pump and probe pulses is varied, where more than two
photons are involved. Ionization times are calculated within the saddle-point
approximations and serve to individualize the different electron wave packets
that produce the RABBIT interferometric scheme. We observe different behaviors
of the phase delays at different intensities of the probe. For example, for
moderate and intense probe fields, the harmonics and sidebands happen to be in
phase ($ \gtrsim 4 \times 10^{11}$ W/cm$^2$). In turn, when the probe field is
sufficiently weak, we recover the well-known rule of thumb for the phase delays
developed within the perturbative RABBIT theory [see D. Guenot et al. Phys.
Rev. A 85, 053424 (2012)]. We show that the intracycle interference of the
different paths contributing to the final energy (sideband or high harmonic) is
responsible for the different behaviors of the interference pattern.
Comparisons with the numerical solution of the strong-field approximation and
time-dependent Schr\"odinger equation confirm the reliability of our
semiclassical non-perturbative theory.
