To get to the core of the galaxy, you need to fly through a very large number of hostile Grox-held systems. Before attempting it, I recommend having the best possible interstellar drive, energy capacity, and health capacity. You will also need about 25 full repair kits and 25 full energy recharge kits. The tool that allows you to fly through black holes is also highly useful.
Some specific suggestions:
- Plan a general route through the most densely-starred corridor you can see. As you get close to the centre of the galaxy, the distance you can travel per jump falls off sharply.
- Don’t waste time attacking any Grox ships or cities. Just fly
- Use a repair pack whenever you are down to 1/3 health. It is a bit wasteful, but makes it less likely you will get blown up and need to start over.
- Black holes are very useful. Once you have ten or so Grox ships attacking you, being able to fly through one and lose them all is quite helpful.
- Keep an eye on the 3D nature of the starfield. Finding a route will be tricky at times.
- Once you have finished your business at the core, the easiest way to get back to your own space is to let yourself get blown up. It is a lot less costly and frustrating than flying back through the whole Grox mass.