  Probing vibronic coherence in molecules has been a central topic in ultrafast
science, as it is an essential prerequisite to monitoring electronic motion.
While experiments have demonstrated that attosecond transient absorption
spectroscopy (ATAS) can probe the vibronic coherence in a few molecules, its
robustness remains largely unexplored. In this Letter, we develop a
comprehensive theory for ATAS which accounts for the orientation dependence of
the density matrix of a pumped molecule. We apply our theory to N$_2^+$ formed
by multiorbital tunnel ionization under a few-cycle intense near-infrared laser
pulse. The simulated x-ray absorption spectrum shows clear signatures of the
vibronic coherence between the $A^2\Pi_u$ and $B^2\Sigma_u^+$ states of
N$_2^+$, which was predicted to be absent by a previous theory. We further
define a coherence contrast factor to quantify the robustness of ATAS. This
work advances the theoretical foundation of ATAS and paves the way for
monitoring electronic motion in generic molecules.
