Symmetry breaking in topological matter has become in recent years a key concept in condensed matter physics to unveil novel electronic states. In this work, we predict that broken inversion symmetry and strong spin-orbit coupling in trigonal PtBi₂ lead to a type-I Weyl semimetal band structure. Transport measurements show an unusually robust low dimensional superconductivity in thin exfoliated flakes up to 126 nm in thickness (with T_c ∼ 275-400 mK), which constitutes the first report and study of unambiguous superconductivity in a type-I Weyl semimetal. Remarkably, a Berezinskii-Kosterlitz-Thouless transition with T_BKT ∼ 310 mK is revealed in up to 60 nm thick flakes, which is nearly an order of magnitude thicker than the rare examples of two-dimensional superconductors exhibiting such a transition. This makes PtBi₂ an ideal platform to study low dimensional and unconventional superconductivity in topological semimetals.