The best way to go for this is to start off collecting $35,000 for the upgraded ship. It is not required but makes the process a tad bit faster and your ship shoots much quicker.
After collecting the money; start from the Crowdkicker spawn point and run through the first two doors and head left to the landing pad then go up the elevator and through the door to your ship.
The controls are absolute garbage and super sensitive so take it slow. The right joystick is to control this ship and it is inverted. The left joystick controls the left paw which is used to speed up and slow down the ship. The down arrow on the left slows down the ship and the up arrow on the right speeds up the ship. Left trigger uses the left paw and then the right trigger shoots.
The red boxes are the pirate ships and I think I killed about 18 ships. After so many it will pop without a problem.
You will want to start from the colony and fly out to each area with 3-5 pirates until the solid boxes turns bigger and then come to a full stop. Position your ship and shoot down the pirate ships. After you shot down the group of pirates turn around and fly back to the colony. If you wish to risk it you can fly closer to the ships and utilize the auto lock but you then run the risk of flying out of bounds and dealing with potential ships shooting you down.
I found most of my headaches were invisible zones/walls that kept me from getting this achievement. Most of the time I randomly ended up in the carrier which takes forever as it loads you into the carrier and then you have to then grab a new ship from the carrier and fly out. Also you could run to the teleporter in the back left of the carrier and from the travel agency run back to landing pad. The worst thing however that happened less often was flying from one area to the next and the game would sent me to a loading screen and then freeze which means you have to reload the game the start all over again from scratch.
Take your time and good luck!