Badge Outta Heck

You gain this badge by defeating the Grox. This is extremely hard to do, even with cheats. The Grox control some 600 to 1,000 systems and thus will take a long while. The Grox possess few weaknesses and have formidable ships so you'll need some help.

Grox Tactical Weaknesses

 * Terraforming planet to T1 will remove the Grox from the system
 * Antimatter weaponry with shield and extreme health
 * Most of Grox's colonies contain only one unfortified city.

Effective Tactics
You have three basic options when trying to defeat the Grox, terraforming, conventional warfare, or planet busting. If you go terraforming Grox into extinction you should have lots of Mega Energy Packs because terraforming takes a lot of energy. If you try beating them like a normal enemy you'll quickly realize you more powerful than standard weaponry. The only weapon that can take out swarms of Grox ships in one shot is the expensive Antimatter Missile. To eliminate cities your best option is using the Antimatter bomb, which can also destroy the enemy in single blast. You'll be in for a long and grueling war, but it is one the most fun! By the way, since your full empire halfway across the galaxy they can only do raids on your planets. The final way is to seriously pack up on Planet Busters and destroy all of their planets. This is immensely expensive but is also the easiest to use. If you cheat and have enough of them, this is your most effective option. Since most of the Grox cities are unfortified with minimal buildings, first fly close to the city to draw the local defense UFOs (as well as the area patrol UFOs if they followed you down to the surface) away, then fly back low and dump a few Mega Bomb at its city hall to destroy the city. Once the city is destroyed, all Grox UFOs will disengage and start to ascend out of the planet. Make sure not to enter the orbit before the area patrol UFOs disappear from the planet's surface, or they will keep attacking you once your UFO enters the orbit.

Possible Weakness
Taking out the Grox home planet is only considered as taking out one of its many colonies. It will randomly(?) choose another planet as its new empire capital after its home planet is conquered. On the side notes, the Grox home planet is simply a T0 planet with 3 partially fortified cities. It is much easier to conquer using conventional warfare compares to other empire home planets with 10 or so fully fortified cities, not to mention terraforming the planet into T1 will wipe 3 cities out instantly.