From the main menu, select "Start", select "Arena I" when it loads, you will be in front of the "Reactor" where you can buy weapons and upgrades. Press LT to access the upgrade menu then use the D-pad to select the Rifle and press A to buy it. Press LT to exit the upgrade menu. Press RB to switch to the Rifle and we are good to go.
Now press RT while in front of the Reactor to start wave 1. Shoot all the enemies until you have completed the wave and then rinse and repeat the RT at the reactor to start new waves until you kill enough enemies to unlock the achievement. Should take about 2-3 minutes.