Islanded microgrids are vulnerable to frequency fluctuations due to the presence of low-inertia distributed energy resources (DERs). Moreover, implementation of both synchronous-based and inverter-based DERs with a significant difference in inertia leads to a power imbalance between generation and consumption during transients. This results in frequency variations which might have severe consequences such as blackouts. This paper develops a control scheme for battery energy storage systems (BESSs) to enhance the dynamic response of islanded microgrids by mitigating the frequency fluctuations. A piecewise linear-elliptic (PLE) droop characteristic is proposed and employed in BESS to achieve a faster power balance between generation and consumption during transients, resulting in enhanced frequency responses. Different case studies are carried out to validate the viability of the proposed approach in improving the dynamics of islanded microgrids.