To unlock the battle game, finish the game and you will get Claire and Chris Redfield playable at the beginning.
Unlock the One Hit Kills option:
Steve: equip the 2 lugers and aim, wait for a zombie and simultaneously press up and shoot to blow of his face
Chris: get his enhanced handgun and stand a bit away from it and shoot
Claire: do the same as with Chris and Steve, but aim high with a powerful weapon