Yeah, the last 2 badges (the ones which are Question marks) both relate to the Grox. One of them is "Dance with the Devil" and that's forming an Alliance with the Grox, and the other is "Badge outta Heck", which is Beating the Grox.
Good luck.
Well I allied with the Grox again just last night, so dang funny when you do, suddenly the left half of your screen is filled with communiques from other worlds, all declaring war on you, and when you pass through any new parts of space, it fills with red bubbles.
One thing is for sure, you hardly ever have to heal the Grox vessel in your fleet, he kicks enough arse on his own.
It's also well worth the feeling of achievement you get, when flying towards the core and all you see is green and hundreds of planets in your alliance.
The key is to make first contact, don't avoid them, establish embassies on the outer rim territories of their space, fly from wormhole to wormhole to get to the core, do as many missions as you can (max points is 50), Super happy ray get's you 30, blow up planets of other races close to their space (50 pts max), turn off your auto turret to avoid blowing up their ships, cloak when on their planets, throw up your shields to avoid destruction when you can... That's about it really, they only have negative 70 points against you to start, and of course, once the face turns blue, start trading (30pts) so it's pretty simple really!
Kind of a garbled walkthrough I just did, I didn't even know I was giving tips till I finished typing it! HAHA 😵