If you have 4 controllers and a rubber band, you can grind this achievement out fairly quickly. (See the end for tips if you don't have 4 controllers)
First, go to the options and change the health to 50%. This will make ships die faster (pretty sure it defaults back to 100% if there are any bots in the match).
You will want to select Gladiator mode, with teams on, infinite lives, and 300 seconds (5 minutes).
For simplicity, you can just pick the default ship and weapon for all players (the ion gun works great for racking up shots anyways).
If you want it to go faster, you can select weaker ships for all of the enemy (check stats).
IMPORTANT: You will want your main profile ship to choose a team that is different from the other 3. When outnumbered 3 to 1 in a team match, your ship will be equipped with additional auto-firing turrets that will ad to your shot count.
For the stage, you will want the Alpha (easy) version of the black hole level (top right of selection screen).
Once the match starts, use a rubber band to hold down the LT. This will continuously fire your fast shooting ion gun. Your turrets will eventually get destroyed, but respawn you time you die. The level is great because it will throw everyone around the screen and help you get kills (and get killed) without having to do anything.
Each round will get about 50 kills or so without you actually having to do anything. You can make it go faster by actually playing the game trying to kill as many enemies as you can.
If you don't have 4 controllers, you can use the controllers you do have (or use bots), but turn Teams off in the settings. You cannot configure a 3 vs 1 mode with bots as they will always attempt to even out the teams.
Below is a video I made showing a similar setup that will help with the grind.