  Coupling between $\sigma$-bonding electrons and phonons is generally very
strong. To metallize $\sigma$-electrons provides a promising route to hunt for
new high-T$_c$ superconductors. Based on this picture and first-principles
density functional calculation with Wannier interpolation for electronic
structure and lattice dynamics, we predict that trilayer film LiB$_2$C$_2$ is a
good candidate to realize this kind of high-T$_c$ superconductivity. By solving
the anisotropic Eliashberg equations, we find that free-standing trilayer
LiB$_2$C$_2$ is a phonon-mediated superconductor with T$_c$ exceeding the
liquid-nitrogen temperature at ambient pressure. The transition temperature can
be further raised to 125 K by applying a biaxial tensile strain.
