This paper considers the Cops and Attacking Robbers game, a variant of Cops and Robbers, where the robber is empowered to attack a cop in the same way a cop can capture the robber. In a graph G , the number of cops required to capture a robber in the Cops and Attacking Robbers game is denoted by cc ( G ) . We give a sufficient condition for a triangle-free graph to have attacking cop number at most 2 and we characterise when outerplanar graphs have attacking cop number 2. We also prove that all bipartite planar graphs G have cc ( G ) ≤ 4 and show this is tight by constructing a bipartite planar graph G with cc ( G ) = 4 . Finally we construct 17 non-isomorphic graphs H of order 58 with cc ( H ) = 6 and c ( H ) = 3 . This provides the first example of a graph H with cc ( H ) − c ( H ) ≥ 3 , extending work by Bonato et al. (2014). We conclude with a list of conjectures and open problems.