The best way is to go to war against another space-stage empire. Flying from planet to planet in enemy territory or/then entering the atmosphere of a home planet is an easy way to have multiple space ships attack you and there are many cities on a home planet so in result many planet defense ships spawn. Having Shield, Mega Proton Missile, and Mega Laser can help, especially in large groups by using the Shield to block attacks, Mega Missiles to do heavy damage, and Mega Laser to do quick strong single damage or to exterminate a fleeing ship. Anti-Matter Missiles are useful but the price will add up over time. Auto Blasters also help since it can shoot multiple ships at once. This helps with the smaller spawned ships in pirate raids.
If you plan to destroy the Grox, you will have to destroy some of their ships sometimes. However, this method is not reccomended as the Grox spaceship have extremely high health and damage.
This can be over multiple save files.
This achievement can easily be earned over time; one simply has to wait for enough pirate/enemy attacks.