Concept:
According to Fajan's rule, small cations with high charge polarize anions → covalent character.
Step 1: Analyze cation size.
Be$^{2+}$ is very small → high polarizing power.
Step 2: Effect on bonding.
Be$^{2+}$ distorts electron cloud of Cl$^-$ → covalent bonding.
Step 3: Conclusion.
BeCl$_2$ is covalent.