Two Aegis shields ftw. Between juggling a 1up and Medikit for most of the game, this group was the most underpowered winners I've ever had.
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Just to add, two Aegis shields are nearly broken. They have near-complete board coverage if they are in adjacent opposite corners in the mid-ranks, and they can save anything from destruction, regardless of type. They're more powerful than the Paramedic for sustaining long-term effects, and if you have things like stasis or medikits they can allow you to maintain an near infinite loop to destroy bigger bosses with inferior units.