  Given a generic stable strongly parabolic $SL(2,\mathbb{C})$-Higgs bundle
$(\mathcal{E}, \varphi)$, we describe the family of harmonic metrics $h_t$ for
the ray of Higgs bundles $(\mathcal{E}, t \varphi)$ for $t\gg0$ by perturbing
from an explicitly constructed family of approximate solutions
$h_t^{\mathrm{app}}$. We then describe the natural hyperK\"ahler metric on
$\mathcal{M}$ by comparing it to a simpler "semi-flat" hyperK\"ahler metric. We
prove that $g_{L^2} - g_{\mathrm{sf}} = O(\mathrm{e}^{-\gamma t})$ along a
generic ray, proving a version of Gaiotto-Moore-Neitzke's conjecture.
  Our results extend to weakly parabolic $SL(2,\mathbb{C})$-Higgs bundles as
well.
  In the case of the four-puncture sphere, we describe the moduli space and
metric more explicitly. In this case, we prove that the hyperk\"ahler metric is
ALG and show that the rate of exponential decay is the conjectured optimal one,
$\gamma=4L$, where $L$ is the length of the shortest geodesic on the base curve
measured in the singular flat metric $|\mathrm{det}\, \varphi|$.
