Eutectic high entropy alloys, with lamellar arrangement of solid solution phases, represent a new paradigm for simultaneously achieving high strength and ductility, thereby circumventing this well-known trade-off in conventional alloys. However, dynamic strengthening mechanisms and phase-boundary interactions during external loading remain unclear for these eutectic systems. In this study, small-scale mechanical behavior was evaluated for AlCoCrFeNi2.1 eutectic high entropy alloy, consisting of a lamellar arrangement of L12 and B2 solid-solution phases. The ultimate tensile strength was 1165 MPa with ductility of ~18% and ultimate compressive strength was 1863 MPa with a total compressive fracture strain of ~34%. Dual mode fracture was observed with ductile failure for L12 phase and brittle mode for B2 phase. Phase-specific mechanical tests using nano-indentation and micro-pillar compression showed higher hardness and strength and larger strain rate sensitivity for B2 compared with L12. Micro-pillars on B2 phase deformed by plastic barreling while L12 micro-pillars showed high density of slip steps due to activation of more slip systems and homogenous plastic flow. Mixed micro-pillars containing both the phases exhibited dual yielding behavior while the interface between L12 and B2 was well preserved without any sign of separation or cracking. Phase-specific friction analysis revealed higher coefficient of friction for B2 compared to L12. These results will pave the way for fundamental understanding of phase-specific contribution to bulk mechanical response of concentrated alloys and help in designing structural materials with high fracture toughness.