  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
$\attCop(G)$. We characterise the triangle-free graphs $G$ with $\attCop(G)
\leq 2$ via a natural generalisation of the cop-win characterisation by
Nowakowski and Winkler \cite{nowakowski1983vertex}. We also prove that all
bipartite planar graphs $G$ have $\attCop(G) \leq 4$ and show this is tight by
constructing a bipartite planar graph $G$ with $\attCop(G) = 4$. Finally we
construct $17$ non-isomorphic graphs $H$ of order $58$ with $\attCop(H) = 6$
and $\cop(H)=3$. This provides the first example of a graph $H$ with
$\attCop(H) - \cop(H) \geq 3$ extending work by Bonato, Finbow, Gordinowicz,
Haidar, Kinnersley, Mitsche, Pra\l{}at, and Stacho \cite{bonato2014robber}. We
conclude with a list of conjectures and open problems.
