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Given a generic stable strongly parabolic $SL(2,\mathbb{C})$-Higgs bundle$(\mathcal{E}, \varphi)$, we describe the family of harmonic metrics $h_t$ forthe ray of Higgs bundles $(\mathcal{E}, t \varphi)$ for $t\gg0$ by perturbingfrom 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. Weprove that $g_{L^2} - g_{\mathrm{sf}} = O(\mathrm{e}^{-\gamma t})$ along ageneric ray, proving a version of Gaiotto-Moore-Neitzke's conjecture.  Our results extend to weakly parabolic $SL(2,\mathbb{C})$-Higgs bundles aswell.  In the case of the four-puncture sphere, we describe the moduli space andmetric more explicitly. In this case, we prove that the hyperk\"ahler metric isALG 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 curvemeasured in the singular flat metric $|\mathrm{det}\, \varphi|$.

Asymptotic Geometry of the Moduli Space of Parabolic $SL(2,\mathbb{C})$-Higgs Bundles