You will encounter the first arcade machine in the bar early in the game, all though I recommend waiting until around mid game when you come to a nightclub with a door that requires 2000 arcade credits to enter, there is an arcade machine in the same room, you should get around 4000 credits for doing all 42 waves. As soon as the game starts just hold RB and LB, that will make the character shoot and shield at the same time so you shouldn't have any problems reaching wave 42. Once you completed wave 42 stop shooting a guy will show up asking for help, if you shoot him you will have to start over. Don't shoot him and achievement is yours.