Refer to the Grox Alliance Tactics page for help. Otherwise, you can download the Grox Expansion Pack and it'll add 1,000 + relationship boost points so you can ally with them instantly across all space stage games.
Break th galactic code around them. You can do it by destroying empty planets with planet buster. After that, use some friendly tools and give them money. Get some missions and when it is blue face (friend) start a trade route for easy win.