Catman and Deadshot win this.
Scenario A) Bullseye brags about never missing. Maybe Deadshot does too. Five seconds into the fight, they kill each other with headshots/heartshots/they make sure the other guy is dead. Catman gets close to Punisher, takes a few shots, but mauls Frank. Those shots might not even hit Catman, so it could be that Frank just takes the wrong end of a savage beating. Catman also has the advantage of having range and agility over Frank. Catman can hit him with knives, because Frank isn't that fast, while Frank can't do the same back because Catman can dodge bullets. So yeah, Catman walks out as the only one alive.
Scenario B) Punisher turns and kills Bullseye (because Frank wouldn't do anything else). Deadshot shoots Punisher.