This paper addresses the design considerations and dexterity evaluation of a novel hybrid two-armed micro-surgical slave robot equipped with intraocular dexterity devices. A unified framework for the kinematic modeling of this robot is presented while using the kinematic constraints stemming from the constrained motion of the eye. An augmented Jacobian describing the kinematics of the eye and the relative motion of each one of the two Intra-Ocular Dexterity Robots (IODR) is presented. Using this framework, the capabilities of this two-armed robot in performing dexterous intraocular operations are evaluated and compared to a similar robot without intra-ocular dexterity. The Kinematic Conditioning Index (KCI) for the proposed robot is shown to be significant. The results presented show an increase of approximately 33% and 47% in translational and rotational KCI respectively.