Puzzle Quest Galactrix

To open up this sidequest, you'll need to progress far enough through the story to complete the Hackerz quest at Ceti VI.

The sidequest is bascially a trek across the map, visiting different locations. You'll need to hack a lot of gates as you go (you probably will unlock the Master Hacker achievement in the process), but don't necessarily need to fight at all for this quest, aside from random battles and hostile systems. As you progress through this sidequest, you'll even gain the ability to run from these encounters via PSI power, so use it if you need to. Of course, the earlier you do this quest the better, because you'll probably have less enemies.

Here's the chain of places you'll need to visit in order, getting a new quest at each place:

Atila Sigma
Pleione Rho
Perseus Sigma
Leo Epsilon
Lacerta Omega
Procyon Epsilon
Musca Epsilon
Typhon Rho

Completion of this sidequest will remove any random battles and stop your ship from being attacked by hostile systems. (Don't worry, you'll still be able to grind for xp if/when you want to, just do a quick battle from the menu screen instead of story mode.)