Easiest way to kill 1000 zombies with your bare hands was to go into the toy store on the first floor of Royal Flush Plaza & grab some fireworks. Go upstairs to Ragazines & grab the magazine for combat (increases damage from hand to hand). Go downstairs and jump the railing into the big craps table (the one with the big dice & security guards). Stand next to the railing & throw fireworks to attract zombies to you. As they stand there trying to hit you just throw haymakers (if you have unlocked that already) & use face smash & pick up & throw to kill them. As far as I can tell, skill moves work as long as you are not holding a weapon. They cannot hit or grab you from the other side of the railing. It took me about 20 minutes to get the trophy. You also unlock a new outfit in your locker (tattered clothes, aka he Shaun of the Dead clothes).