If you have 4 controllers and a rubber band, you can grind this achievement out in about 9 hours. (See the end for tips if you don't have 4 controllers)
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).
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 of this mode should net you around 5,000 shots, or 1% of the achievement. You will have to do this around 100 times. Also goes along with 1000 games played and 2,000 players killed.
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.