We study numerically a one-dimensional mixture of spin-$\frac{1}{2}$ fermions and scalar bosons in the hard-core limit. Considering repulsive fermion-fermion and boson-fermion interactions, we find superfluid and insulator states, and determine the boundaries between them calculating several phase diagrams. We determine that, given a fermionic density ${\ensuremath{\rho}}_{F}$, the insulator states are located at the bosonic densities ${\ensuremath{\rho}}_{B}=1\ensuremath{-}{\ensuremath{\rho}}_{F}$ and $1\ensuremath{-}\frac{1}{2}{\ensuremath{\rho}}_{F}$, and emerge even in the absence of fermion-fermion coupling. In addition, the boson-fermion repulsion drives quantum phase transitions inside the insulator lobes with ${\ensuremath{\rho}}_{B}=1/2$. Our predictions could be observed in current cold-atom experimental platforms.